Gapless spin-fluid ground state in a random quantum Heisenberg magnet

Optimally scrambling chiral spin-chain with effective black hole geometry

There is currently significant interest in emulating the essential characteristics of black holes, such as their Hawking radiation or their optimal scrambling behavior, using condensed matter models. In this article, we investigate a chiral spin-chain, whose mean field theory effectively captures the behavior of Dirac fermions in the curved spacetime geometry of a black hole. We find that within the region of the chain that describe the interior of the black hole, strong correlations prevail giving rise to many-body chaotic dynamics. Employing out-of-time-order correlations as a diagnostic tool, we numerically compute the associated Lyapunov exponent. Intriguingly, we observe a linear increase in the Lyapunov exponent with temperature within the black hole's interior at low temperatures, indicative of optimal scrambling behavior. This contrasts with the quadratic temperature dependence exhibited by the spin-chain on the region outside the black hole. Our findings contribute to a deeper understanding of the interplay between black hole geometry and quantum chaos, offering insights into fundamental aspects of quantum gravity.

CUT-E as a 1/N expansion for multiscale molecular polariton dynamics

Molecular polaritons arise when the collective coupling between an ensemble of N molecules and an optical mode exceeds individual photon and molecular linewidths. The complexity of their description stems from their multiscale nature, where the local dynamics of each molecule can, in principle, be influenced by the collective behavior of the entire ensemble. To address this, we previously introduced a formalism called collective dynamics using truncated equations (CUT-E). CUT-E approaches the problem in two stages. First, it exploits permutational symmetries to obtain a substantial simplification of the problem. However, this is often insufficient for parameter regimes relevant to most experiments. Second, it takes the exact solution of the problem in the N → ∞ limit as a reference and derives systematic finite-N corrections. Here, we provide a novel derivation of CUT-E based on recently developed bosonization techniques. We lay down its connections with 1/N expansions that are ubiquitous in other fields of physics and present previously unexplored key aspects of this formalism, including various types of approximations and extensions to high-excitation manifolds.

Quantum chaos, integrability, and late times in the Krylov basis

Quantum chaotic systems are conjectured to display a spectrum whose fine-grained features (gaps and correlations) are well described by random matrix theory (RMT). We propose and develop a complementary version of this conjecture: quantum chaotic systems display a Lanczos spectrum whose local means and covariances are well described by RMT. To support this proposal, we first demonstrate its validity in examples of chaotic and integrable systems. We then show that for Haar-random initial states in RMTs the mean and covariance of the Lanczos spectrum suffice to produce the full long-time behavior of general survival probabilities including the spectral form factor, as well as the spread complexity. In addition, for initial states with continuous overlap with energy eigenstates, we analytically find the long-time averages of the probabilities of Krylov basis elements in terms of the mean Lanczos spectrum. This analysis suggests a notion of eigenstate complexity, the statistics of which differentiate integrable systems and classes of quantum chaos. Finally, we clarify the relation between spread complexity and the universality classes of RMT by exploring various values of the Dyson index and Poisson distributed spectra.

Defect Conformal Field Theory from Sachdev-Ye-Kitaev Interactions

The coupling between defects and extended critical degrees of freedom gives rise to the intriguing theory known as defect conformal field theory (CFT). In this work, we introduce a novel family of boundary and interface CFTs by coupling N Majorana chains with SYK_{q} interactions at the defect. Our analysis reveals that the interaction with q=2 constitutes a new marginal defect. Employing a versatile saddle-point method, we compute unique entanglement characterizations, including the g function and effective central charge, of the defect CFT. Furthermore, we analytically evaluate the transmission coefficient using CFT techniques. Surprisingly, the transmission coefficient deviates from the universal relation with the effective central charge across the defect at the large N limit, suggesting that our defect CFT extends beyond all known examples of Gaussian defect CFT.

From Chaos to Integrability in Double Scaled Sachdev-Ye-Kitaev Model via a Chord Path Integral

We study thermodynamic phase transitions between integrable and chaotic dynamics. We do so by analyzing models that interpolate between the chaotic double scaled Sachdev-Ye-Kitaev (SYK) and the integrable p-spin systems, in a limit where they are described by chord diagrams. We develop a path integral formalism by coarse graining over the diagrams, which we use to argue that the system has two distinct phases: one is continuously connected to the chaotic system, and the other to the integrable. They are separated by a line of first order transition that ends at some finite temperature.

Sparsity-Independent Lyapunov Exponent in the Sachdev-Ye-Kitaev Model

The saturation of a recently proposed universal bound on the Lyapunov exponent has been conjectured to signal the existence of a gravity dual. This saturation occurs in the low-temperature limit of the dense Sachdev-Ye-Kitaev (SYK) model, N Majorana fermions with q body (q>2) infinite-range interactions. We calculate certain out-of-time-order correlators (OTOCs) for N≤64 fermions for a highly sparse SYK model and find no significant dependence of the Lyapunov exponent on sparsity up to near the percolation limit where the Hamiltonian breaks up into blocks. This provides strong support to the saturation of the Lyapunov exponent in the low-temperature limit of the sparse SYK. A key ingredient to reaching N=64 is the development of a novel quantum spin model simulation library that implements highly optimized matrix-free Krylov subspace methods on graphical processing units. This leads to a significantly lower simulation time as well as vastly reduced memory usage over previous approaches, while using modest computational resources. Strong sparsity-driven statistical fluctuations require both the use of a much larger number of disorder realizations with respect to the dense limit and a careful finite size scaling analysis. The saturation of the bound in the sparse SYK points to the existence of a gravity analog that would enlarge substantially the number of field theories with this feature.

Transport properties in non-Fermi liquid phases of nodal-point semimetals

In this review, we survey the current progress in computing transport properties in semimetals which harbour non-Fermi liquid (NFL) phases. We first discuss the widely-used Kubo formalism, which can be applied to the effective theory describing the stable NFL phase obtained via a renormalization group procedure and, hence, is applicable for temperatures close to zero (e.g. optical conductivity). For finite-temperature regimes, which apply to the computations of the generalized DC conductivity tensors, we elucidate the memory matrix approach. This approach is based on an effective hydrodynamic description of the system, and is especially suited for tackling transport calculations in strongly-interacting quantum field theories, because it does not rely on the existence of long-lived quasiparticles. As a concrete example, we apply these two approaches to find the response of the so-calledLuttinger-Abrikosov-Benelavskii phaseof isotropic three-dimensional Luttinger semimetals, which arises under the effects of long-ranged (unscreened) Coulomb interactions, with the chemical potential fine-tuned to cut exactly the nodal point. In particular, we focus on the electric conductivity tensors, thermal and thermoelectric response, Raman response, free energy, entropy density, and shear viscosity.

Exact Numerical Solution of the Fully Connected Classical and Quantum Heisenberg Spin Glass

We present the mean field solution of the quantum and classical Heisenberg spin glasses, using the combination of a high precision numerical solution of the Parisi full replica symmetry breaking equations and a continuous time quantum Monte Carlo algorithm. We characterize the spin glass order and its low-energy excitations down to zero temperature. The Heisenberg spin glass has a rougher energy landscape than its Ising analog, and exhibits a very slow temperature evolution of its dynamical properties. We extend our analysis to the doped, metallic Heisenberg spin glass, which displays unexpectedly slow spin dynamics, reflecting the proximity to the melting quantum critical point and its associated Sachdev-Ye-Kitaev Planckian dynamics.

Magneto-Thermoelectric Transport in Graphene Quantum Dot with Strong Correlations

Disorder at etched edges of graphene quantum dots (GQD) enables random all-to-all interactions between localized charges in partially filled Landau levels, providing a potential platform to realize the Sachdev-Ye-Kitaev (SYK) model. We use quantum Hall edge states in the graphene electrodes to measure electrical conductance and thermoelectric power across the GQD. In specific temperature ranges, we observe a suppression of electric conductance fluctuations and slowly decreasing thermoelectric power across the GQD with increasing temperature, consistent with recent theory for the SYK regime.

Tunable Non-Fermi Liquid Phase from Coupling to Two-Level Systems

We study a controlled large-N theory of electrons coupled to dynamical two-level systems (TLSs) via spatially random interactions. Such a physical situation arises when electrons scatter off low-energy excitations in a metallic glass, such as a charge or stripe glass. Our theory is governed by a non-Gaussian saddle point, which maps to the celebrated spin-boson model. By tuning the coupling strength we find that the model crosses over from a Fermi liquid at weak coupling to an extended region of non-Fermi liquid behavior at strong coupling, and realizes a marginal Fermi liquid at the crossover. Our results are valid for generic space dimensions d>1.

Entanglement in Interacting Majorana Chains and Transitions of von Neumann Algebras

We consider Majorana lattices with two-site interactions consisting of a general function of the fermion bilinear. The models are exactly solvable in the limit of a large number of on-site fermions. The four-site chain exhibits a quantum phase transition controlled by the hopping parameters and manifests itself in a discontinuous entanglement entropy, obtained by constraining the one-sided modular Hamiltonian. Inspired by recent work within the AdS/CFT correspondence, we identify transitions between types of von Neumann operator algebras throughout the phase diagram. We find transitions of the form II_{1}↔III↔I_{∞} that reduce to II_{1}↔I_{∞} in the strongly interacting limit, where they connect nonfactorized and factorized ground states. Our results provide novel realizations of such transitions in a controlled many-body model.

Quantum information scrambling in two-dimensional Bose-Hubbard lattices

It is a well-understood fact that the transport of excitations throughout a lattice is intimately governed by the underlying structures. Hence, it is only natural to recognize that the dispersion of information also has to depend on the lattice geometry. In the present work, we demonstrate that two-dimensional lattices described by the Bose-Hubbard model exhibit information scrambling for systems as little as two hexagons. However, we also find that the out-of-time-ordered correlator (OTOC) shows the exponential decay characteristic for quantum chaos only for a judicious choice of local observables. More generally, the OTOC is better described by Gaussian-exponential convolutions, which alludes to the close similarity of information scrambling and decoherence theory.

Chaos and anomalous transport in a semiclassical Bose-Hubbard chain

We study chaotic dynamics and anomalous transport in a Bose-Hubbard chain in the semiclassical regime (the limit when the number of particles goes to infinity). We find that the system has mixed phase space with both regular and chaotic dynamics, even for long chains with up to 100 wells. The consequence of the mixed phase space is strongly anomalous diffusion in the space of occupation numbers, with a discrete set of transport exponents. After very long times the system crosses over to the hydrodynamic regime with normal diffusion. Anomalous transport is quite universal and almost completely independent of the parameters of the model (Coulomb interaction and chemical potential): It is mainly determined by the initial distribution of particles along the chain. We corroborate our findings by analytical arguments: scaling analysis for the anomalous regime and the Langevin equation for the normal diffusion regime.

Parisi's Hypercube, Fock-Space Frustration, and Near-AdS_{2}/Near-CFT_{1} Holography

We consider a model of Parisi where a single particle hops on an infinite-dimensional hypercube, under the influence of a uniform but disordered magnetic flux. We reinterpret the hypercube as the Fock-space graph of a many-body Hamiltonian and the flux as a frustration of the return amplitudes in Fock-space. We will identify the set of observables that have the same correlation functions as the double-scaled Sachdev-Ye-Kitaev (DS-SYK) model, and hence the hypercube model is an equally good quantum model for near-AdS_{2}/near-CFT_{1} (NAdS_{2}/NCFT_{1}) holography. Unlike the SYK model, the hypercube Hamiltonian is not p local. Instead, the SYK model can be understood as a Fock-space model with similar frustrations. Hence we propose this type of Fock-space frustration as the broader characterization for NAdS_{2}/NCFT_{1} microscopics, which encompasses the hypercube and the DS-SYK models as two specific examples. We then speculate on the possible origin of such frustrations.

Sixfold Way of Traversable Wormholes in the Sachdev-Ye-Kitaev Model

In the infrared limit, a nearly anti-de Sitter spacetime in two dimensions (AdS_{2}) perturbed by a weak double trace deformation and a two-site (q>2)-body Sachdev-Ye-Kitaev (SYK) model with N Majoranas and a weak 2r-body intersite coupling share the same near-conformal dynamics described by a traversable wormhole. We exploit this relation to propose a symmetry classification of traversable wormholes depending on N, q, and r, with q>2r, and confirm it by a level statistics analysis using exact diagonalization techniques. Intriguingly, a time-reversed state never results in a new state, so only six universality classes occur-A, AI, BDI, CI, C, and D-and different symmetry sectors of the model may belong to distinct universality classes.

Classical route to ergodicity and scarring in collective quantum systems

Ergodicity, a fundamental concept in statistical mechanics, is not yet a fully understood phenomena for closed quantum systems, particularly its connection with the underlying chaos. In this review, we consider a few examples of collective quantum systems to unveil the intricate relationship of ergodicity as well as its deviation due to quantum scarring phenomena with their classical counterpart. A comprehensive overview of classical and quantum chaos is provided, along with the tools essential for their detection. Furthermore, we survey recent theoretical and experimental advancements in the domain of ergodicity and its violations. This review aims to illuminate the classical perspective of quantum scarring phenomena in interacting quantum systems.

Effects of topological and non-topological edge states on information propagation and scrambling in a Floquet spin chain

The action of any local operator on a quantum system propagates through the system carrying the information of the operator. This is usually studied via the out-of-time-order correlator (OTOC). We numerically study the information propagation from one end of a periodically driven spin-1/2XYchain with open boundary conditions using the Floquet infinite-temperature OTOC. We calculate the OTOC for two different spin operators,σxandσz. For sinusoidal driving, the model can be shown to host different types of edge states, namely, topological (Majorana) edge states and non-topological edge states. We observe a localization of information at the edge for bothσzandσxOTOCs whenever edge states are present. In addition, in the case of non-topological edge states, we see oscillations of the OTOC in time near the edge, the oscillation period being inversely proportional to the gap between the Floquet eigenvalues of the edge states. We provide an analytical understanding of these effects due to the edge states. It was known earlier that the OTOC for the spin operator which is local in terms of Jordan-Wigner fermions (σz) shows no signature of information scrambling inside the light cone of propagation, while the OTOC for the spin operator which is non-local in terms of Jordan-Wigner fermions (σx) shows signatures of scrambling. We report a remarkable 'unscrambling effect' in theσxOTOC after reflections from the ends of the system. Finally, we demonstrate that the information propagates into the system mainly via the bulk states with the maximum value of the group velocity, and we show how this velocity is controlled by the driving frequency and amplitude.

Instantons and the quantum bound to chaos

The rate at which information scrambles in a quantum system can be quantified using out-of-time-ordered correlators. A remarkable prediction is that the associated Lyapunov exponent [Formula: see text] that quantifies the scrambling rate in chaotic systems obeys a universal bound [Formula: see text]. Previous numerical and analytical studies have indicated that this bound has a quantum-statistical origin. Here, we use path-integral techniques to show that a minimal theory to reproduce this bound involves adding contributions from quantum thermal fluctuations (describing quantum tunneling and zero-point energy) to classical dynamics. By propagating a model quantum-Boltzmann-conserving classical dynamics for a system with a barrier, we show that the bound is controlled by the stability of thermal fluctuations around the barrier instanton (a delocalized structure which dominates the tunneling statistics). This stability requirement appears to be general, implying that there is a close relation between the formation of instantons, or related delocalized structures, and the imposition of the quantum-chaos bound.

A criterion for strange metallicity in the Lorenz ratio

The Wiedemann-Franz (WF) law, stating that the Lorenz ratio L = κ/(Tσ) between the thermal and electrical conductivities in a metal approaches a universal constant L 0 = π 2 k B 2 / ( 3 e 2 ) at low temperatures, is often interpreted as a signature of fermionic Landau quasi-particles. In contrast, we show that various models of weakly disordered non-Fermi liquids also obey the WF law at T → 0. Instead, we propose using the leading low-temperature correction to the WF law, L(T) - L0 (proportional to the inelastic scattering rate), to distinguish different types of strange metals. As an example, we demonstrate that in a solvable model of a marginal Fermi-liquid, L(T) - L0 ∝ - T. Using the quantum Boltzmann equation (QBE) approach, we find analogous behavior in a class of marginal- and non-Fermi liquids with a weakly momentum-dependent inelastic scattering. In contrast, in a Fermi-liquid, L(T) - L0 is proportional to - T2. This holds even when the resistivity grows linearly with T, due to T - linear quasi-elastic scattering (as in the case of electron-phonon scattering at temperatures above the Debye frequency). Finally, by exploiting the QBE approach, we demonstrate that the transverse Lorenz ratio, Lxy = κxy/(Tσxy), exhibits the same behavior.

Random coupling model of turbulence as a classical Sachdev-Ye-Kitaev model

We point out that a classical analog of the Sachdev-Ye-Kitaev (SYK) model, a solvable model of quantum many-body chaos, was studied long ago in the turbulence literature. Motivated by the Navier-Stokes equation in the turbulent regime and the nonlinear Schrödinger equation describing plasma turbulence, in which there is mixing between many different modes, the random coupling model has a Gaussian-random coupling between any four of a large number N of modes. The model was solved in the 1960s, before the introduction of large-N path-integral techniques, using a method referred to as the direct interaction approximation. We use the path integral to derive the effective action for the model. The large-N saddle gives an integral equation for the two-point function, which is very similar to the corresponding equation in the SYK model. The connection between the SYK model and the random coupling model may, on the one hand, provide new physical contexts in which to realize the SYK model and, on the other hand, suggest new models of turbulence and techniques for studying them.

Operator Growth in Open Quantum Systems

The spreading of quantum information in closed systems, often termed scrambling, is a hallmark of many-body quantum dynamics. In open systems, scrambling competes with noise, errors, and decoherence. Here, we provide a universal framework that describes the scrambling of quantum information in open systems: we predict that the effect of open-system dynamics is fundamentally controlled by operator size distributions and independent of the microscopic error mechanism. This framework allows us to demonstrate that open quantum systems exhibit universal classes of information dynamics that fundamentally differ from their unitary counterparts. Implications for the Loschmidt echo, nuclear magnetic resonance experiments, and the classical simulability of open quantum dynamics will be discussed.

Universality in long-distance geometry and quantum complexity

In physics, two systems that radically differ at short scales can exhibit strikingly similar macroscopic behaviour: they are part of the same long-distance universality class1. Here we apply this viewpoint to geometry and initiate a program of classifying homogeneous metrics on group manifolds2 by their long-distance properties. We show that many metrics on low-dimensional Lie groups have markedly different short-distance properties but nearly identical distance functions at long distances, and provide evidence that this phenomenon is even more robust in high dimensions. An application of these ideas of particular interest to physics and computer science is complexity geometry3-7-the study of quantum computational complexity using Riemannian geometry. We argue for the existence of a large universality class of definitions of quantum complexity, each linearly related to the other, a much finer-grained equivalence than typically considered. We conjecture that a new effective metric emerges at larger complexities that describes a broad class of complexity geometries, insensitive to various choices of microscopic penalty factors. We discuss the implications for recent conjectures in quantum gravity.

Mutual information of spin systems from autoregressive neural networks

We describe a direct method to estimate the bipartite mutual information of a classical spin system based on Monte Carlo sampling enhanced by autoregressive neural networks. It enables us to study arbitrary geometries of subsystems, and it can be generalized to classical field theories. We demonstrate it on the Ising model for four partitionings, including a multiply connected even-odd division. We show that the area law is satisfied for temperatures away from the critical temperature: the constant term is universal, whereas the proportionality coefficient is different for the even-odd partitioning.

Coulomb Drag and Heat Transfer in Strange Metals

We address Coulomb drag and near-field heat transfer in a double-layer system of incoherent metals. Each layer is modeled by an array of tunnel-coupled SYK dots with random interlayer interactions. Depending on the strength of intradot interactions and interdot tunneling, this model captures the crossover from the Fermi liquid to a strange metal phase. The absence of quasiparticles in the strange metal leads to temperature-independent drag resistivity, which is in strong contrast with the quadratic temperature dependence in the Fermi liquid regime. We show that all the parameters can be independently measured in near-field heat transfer experiments, performed in Fermi liquid and strange metal regimes.

Universal theory of strange metals from spatially random interactions

Strange metals-ubiquitous in correlated quantum materials-transport electrical charge at low temperatures but not by the individual electronic quasiparticle excitations, which carry charge in ordinary metals. In this work, we consider two-dimensional metals of fermions coupled to quantum critical scalars, the latter representing order parameters or fractionalized particles. We show that at low temperatures (T), such metals generically exhibit strange metal behavior with a T-linear resistivity arising from spatially random fluctuations in the fermion-scalar Yukawa couplings about a nonzero spatial average. We also find a T ln(1/T) specific heat and a rationale for the Planckian bound on the transport scattering time. These results are in agreement with observations and are obtained in the large N expansion of an ensemble of critical metals with N fermion flavors.

Generalized Thermalization in Quantum-Chaotic Quadratic Hamiltonians

Thermalization (generalized thermalization) in nonintegrable (integrable) quantum systems requires two ingredients: equilibration and agreement with the predictions of the Gibbs (generalized Gibbs) ensemble. We prove that observables that exhibit eigenstate thermalization in single-particle sector equilibrate in many-body sectors of quantum-chaotic quadratic models. Remarkably, the same observables do not exhibit eigenstate thermalization in many-body sectors (we establish that there are exponentially many outliers). Hence, the generalized Gibbs ensemble is generally needed to describe their expectation values after equilibration, and it is characterized by Lagrange multipliers that are smooth functions of single-particle energies.

Solvable models of quantum black holes: a review on Jackiw-Teitelboim gravity

We review recent developments in Jackiw-Teitelboim gravity. This is a simple solvable model of quantum gravity in two dimensions (that arises e.g. from the s-wave sector of higher dimensional gravity systems with spherical symmetry). Due to its solvability, it has proven to be a fruitful toy model to analyze important questions such as the relation between black holes and chaos, the role of wormholes in black hole physics and holography, and the way in which information that falls into a black hole can be recovered.

Can Neural Quantum States Learn Volume-Law Ground States?

We study whether neural quantum states based on multilayer feed-forward networks can find ground states which exhibit volume-law entanglement entropy. As a testbed, we employ the paradigmatic Sachdev-Ye-Kitaev model. We find that both shallow and deep feed-forward networks require an exponential number of parameters in order to represent the ground state of this model. This demonstrates that sufficiently complicated quantum states, although being physical solutions to relevant models and not pathological cases, can still be difficult to learn to the point of intractability at larger system sizes. Hence, the variational neural network approach offers no benefits over exact diagonalization methods in this case. This highlights the importance of further investigations into the physical properties of quantum states amenable to an efficient neural representation.

Engineering SYK Interactions in Disordered Graphene Flakes under Realistic Experimental Conditions

We model interactions following the Sachdev-Ye-Kitaev (SYK) framework in disordered graphene flakes up to 300 000 atoms in size (∼100  nm in diameter) subjected to an out-of-plane magnetic field B of 5-20 Tesla within the tight-binding formalism. We investigate two sources of disorder: (i) irregularities at the system boundaries, and (ii) bulk vacancies-for a combination of which we find conditions that could be favorable for the formation of the phase with Sachdev-Ye-Kitaev features under realistic experimental conditions above the liquid helium temperature.

Controlling Local Thermalization Dynamics in a Floquet-Engineered Dipolar Ensemble

Understanding the microscopic mechanisms of thermalization in closed quantum systems is among the key challenges in modern quantum many-body physics. We demonstrate a method to probe local thermalization in a large-scale many-body system by exploiting its inherent disorder and use this to uncover the thermalization mechanisms in a three-dimensional, dipolar-interacting spin system with tunable interactions. Utilizing advanced Hamiltonian engineering techniques to explore a range of spin Hamiltonians, we observe a striking change in the characteristic shape and timescale of local correlation decay as we vary the engineered exchange anisotropy. We show that these observations originate from the system's intrinsic many-body dynamics and reveal the signatures of conservation laws within localized clusters of spins, which do not readily manifest using global probes. Our method provides an exquisite lens into the tunable nature of local thermalization dynamics and enables detailed studies of scrambling, thermalization, and hydrodynamics in strongly interacting quantum systems.

Reconciling scaling of the optical conductivity of cuprate superconductors with Planckian resistivity and specific heat

Materials tuned to a quantum critical point display universal scaling properties as a function of temperature T and frequency ω. A long-standing puzzle regarding cuprate superconductors has been the observed power-law dependence of optical conductivity with an exponent smaller than one, in contrast to T-linear dependence of the resistivity and ω-linear dependence of the optical scattering rate. Here, we present and analyze resistivity and optical conductivity of La_2-xSr_xCuO₄ with x = 0.24. We demonstrate ℏω/k_BT scaling of the optical data over a wide range of frequency and temperature, T-linear resistivity, and optical effective mass proportional to [Formula: see text] corroborating previous specific heat experiments. We show that a T, ω-linear scaling Ansatz for the inelastic scattering rate leads to a unified theoretical description of the experimental data, including the power-law of the optical conductivity. This theoretical framework provides new opportunities for describing the unique properties of quantum critical matter.

SU(2)-Symmetric Spin-Boson Model: Quantum Criticality, Fixed-Point Annihilation, and Duality

The annihilation of two intermediate-coupling renormalization-group (RG) fixed points is of interest in diverse fields from statistical mechanics to high-energy physics, but has so far only been studied using perturbative techniques. Here we present high-accuracy quantum Monte Carlo results for the SU(2)-symmetric S=1/2 spin-boson (or Bose-Kondo) model. We study the model with a power-law bath spectrum ∝ω^{s} where, in addition to a critical phase predicted by perturbative RG, a stable strong-coupling phase is present. Using a detailed scaling analysis, we provide direct numerical evidence for the collision and annihilation of two RG fixed points at s^{*}=0.6540(2), causing the critical phase to disappear for s<s^{*}. In particular, we uncover a surprising duality between the two fixed points, corresponding to a reflection symmetry of the RG beta function, which we utilize to make analytical predictions at strong coupling which are in excellent agreement with numerics. Our work makes phenomena of fixed-point annihilation accessible to large-scale simulations, and we comment on the consequences for impurity moments in critical magnets.

Quantum Bounds on the Generalized Lyapunov Exponents

We discuss the generalized quantum Lyapunov exponents Lq, defined from the growth rate of the powers of the square commutator. They may be related to an appropriately defined thermodynamic limit of the spectrum of the commutator, which plays the role of a large deviation function, obtained from the exponents Lq via a Legendre transform. We show that such exponents obey a generalized bound to chaos due to the fluctuation-dissipation theorem, as already discussed in the literature. The bounds for larger q are actually stronger, placing a limit on the large deviations of chaotic properties. Our findings at infinite temperature are exemplified by a numerical study of the kicked top, a paradigmatic model of quantum chaos.

Hamiltonian Simulation with Random Inputs

The algorithmic error of digital quantum simulations is usually explored in terms of the spectral norm distance between the actual and ideal evolution operators. In practice, this worst-case error analysis may be unnecessarily pessimistic. To address this, we develop a theory of average-case performance of Hamiltonian simulation with random initial states. We relate the average-case error to the Frobenius norm of the multiplicative error and give upper bounds for the product formula (PF) and truncated Taylor series methods. As applications, we estimate average-case error for the digital Hamiltonian simulation of general lattice Hamiltonians and k-local Hamiltonians. In particular, for the nearest-neighbor Heisenberg chain with n spins, the error is quadratically reduced from O(n) in the worst case to O(sqrt[n]) on average for both the PF method and the Taylor series method. Numerical evidence suggests that this theory accurately characterizes the average error for concrete models. We also apply our results to error analysis in the simulation of quantum scrambling.

Relaxation Exponents of OTOCs and Overlap with Local Hamiltonians

OTOC has been used to characterize the information scrambling in quantum systems. Recent studies have shown that local conserved quantities play a crucial role in governing the relaxation dynamics of OTOC in non-integrable systems. In particular, the slow scrambling of OTOC is seen for observables that have an overlap with local conserved quantities. However, an observable may not overlap with the Hamiltonian but instead with the Hamiltonian elevated to an exponent larger than one. Here, we show that higher exponents correspond to faster relaxation, although still algebraic, and such exponents can increase indefinitely. Our analytical results are supported by numerical experiments.

Superconductor-Insulator Transition in a Non-Fermi Liquid

We present a model of a strongly correlated system with a non-Fermi liquid high temperature phase. Its ground state undergoes an insulator to superconductor quantum phase transition (QPT) as a function of a pairing interaction strength. Both the insulator and the superconductor are originating from the same interaction mechanism. The resistivity in the insulating phase exhibits the activation behavior with the activation energy, which goes to zero at the QPT. This leads to a wide quantum critical regime with an algebraic temperature dependence of the resistivity. Upon raising the temperature in the superconducting phase, the model exhibits a finite temperature phase transition to a Bose metal phase, which separates the superconductor from the non-Fermi liquid metal.

Traversable wormhole dynamics on a quantum processor

The holographic principle, theorized to be a property of quantum gravity, postulates that the description of a volume of space can be encoded on a lower-dimensional boundary. The anti-de Sitter (AdS)/conformal field theory correspondence or duality1 is the principal example of holography. The Sachdev-Ye-Kitaev (SYK) model of N ≫ 1 Majorana fermions2,3 has features suggesting the existence of a gravitational dual in AdS2, and is a new realization of holography4-6. We invoke the holographic correspondence of the SYK many-body system and gravity to probe the conjectured ER=EPR relation between entanglement and spacetime geometry7,8 through the traversable wormhole mechanism as implemented in the SYK model9,10. A qubit can be used to probe the SYK traversable wormhole dynamics through the corresponding teleportation protocol9. This can be realized as a quantum circuit, equivalent to the gravitational picture in the semiclassical limit of an infinite number of qubits9. Here we use learning techniques to construct a sparsified SYK model that we experimentally realize with 164 two-qubit gates on a nine-qubit circuit and observe the corresponding traversable wormhole dynamics. Despite its approximate nature, the sparsified SYK model preserves key properties of the traversable wormhole physics: perfect size winding11-13, coupling on either side of the wormhole that is consistent with a negative energy shockwave14, a Shapiro time delay15, causal time-order of signals emerging from the wormhole, and scrambling and thermalization dynamics16,17. Our experiment was run on the Google Sycamore processor. By interrogating a two-dimensional gravity dual system, our work represents a step towards a program for studying quantum gravity in the laboratory. Future developments will require improved hardware scalability and performance as well as theoretical developments including higher-dimensional quantum gravity duals18 and other SYK-like models19.

Ground-state energy distribution of disordered many-body quantum systems

Extreme-value distributions are studied in the context of a broad range of problems, from the equilibrium properties of low-temperature disordered systems to the occurrence of natural disasters. Our focus here is on the ground-state energy distribution of disordered many-body quantum systems. We derive an analytical expression that, upon tuning a parameter, reproduces with high accuracy the ground-state energy distribution of the systems that we consider. For some models, it agrees with the Tracy-Widom distribution obtained from Gaussian random matrices. They include transverse Ising models, the Sachdev-Ye model, and a randomized version of the PXP model. For other systems, such as Bose-Hubbard models with random couplings and the disordered spin-1/2 Heisenberg chain used to investigate many-body localization, the shapes are at odds with the Tracy-Widom distribution. Our analytical expression captures all of these distributions, thus playing a role to the lowest energy level similar to that played by the Brody distribution to the bulk of the spectrum.

Statistical complexity and the road to equilibrium in many-body chaotic quantum systems

In this work we revisit the problem of equilibration in isolated many-body interacting quantum systems. We pay particular attention to quantum chaotic Hamiltonians, and rather than focusing on the properties of the asymptotic states and how they adhere to the predictions of the Eigenstate Thermalization Hypothesis, we focus on the equilibration process itself, i.e., the road to equilibrium. Along the road to equilibrium the diagonal ensembles obey an emergent form of the second law of thermodynamics and we provide an information theoretic proof of this fact. With this proof at hand we show that the road to equilibrium is nothing but a hierarchy in time of diagonal ensembles. Furthermore, introducing the notions of statistical complexity and the entropy-complexity plane, we investigate the uniqueness of the road to equilibrium in a generic many-body system by comparing its trajectories in the entropy-complexity plane to those generated by a random Hamiltonian. Finally, by treating the random Hamiltonian as a perturbation we analyzed the stability of entropy-complexity trajectories associated with the road to equilibrium for a chaotic Hamiltonian and different types of initial states.

Onset of Quantum Chaos in Random Field Theories

We study the quantum Lyapunov exponent λ_{L} in theories with spacetime-independent disorder. We first derive self-consistency equations for the two- and four-point functions for products of N models coupled by disorder at large N, generalizing the equations appearing in SYK-like models. We then study families of theories in which the disorder coupling is an exactly marginal deformation, allowing us to follow λ_{L} from weak to strong coupling. We find interesting behaviors, including a discontinuous transition into chaos, mimicking classical KAM theory.

Critical metallic phase in the overdoped random t-J model

We investigate a model of electrons with random and all-to-all hopping and spin exchange interactions, with a constraint of no double occupancy. The model is studied in a Sachdev-Ye-Kitaev-like large-M limit with SU(M) spin symmetry. The saddle-point equations of this model are similar to approximate dynamic mean-field equations of realistic, nonrandom, t-J models. We use numerical studies on both real and imaginary frequency axes, along with asymptotic analyses, to establish the existence of a critical non-Fermi-liquid metallic ground state at large doping, with the spin correlation exponent varying with doping. This critical solution possesses a time-reparameterization symmetry, akin to Sachdev-Ye-Kitaev (SYK) models, which contributes a linear-in-temperature resistivity over the full range of doping where the solution is present. It is therefore an attractive mean-field description of the overdoped region of cuprates, where experiments have observed a linear-T resistivity in a broad region. The critical metal also displays a strong particle-hole asymmetry, which is relevant to Seebeck coefficient measurements. We show that the critical metal has an instability to a low-doping spin-glass phase and compute a critical doping value. We also describe the properties of this metallic spin-glass phase.

Stranger than metals

In traditional metals, the temperature ( T ) dependence of electrical resistivity vanishes at low or high T , albeit for different reasons. Here, we review a class of materials, known as “strange” metals, that can violate both of these principles. In strange metals, the change in slope of the resistivity as the mean free path drops below the lattice constant, or as T → 0, can be imperceptible, suggesting continuity between the charge carriers at low and high T . We focus on transport and spectroscopic data on candidate strange metals in an effort to isolate and identify a unifying physical principle. Special attention is paid to quantum criticality, Planckian dissipation, Mottness, and whether a new gauge principle is needed to account for the nonlocal transport seen in these materials.

Disordered Vector Models: From Higher Spins to Incipient Strings

We present a one-parameter family of large N disordered models, with and without supersymmetry, in three spacetime dimensions. They interpolate from the critical large N vector model dual to a classical higher spin theory toward a theory with a classical string dual. We analyze the spectrum and operator product expansion data of the theories. While the supersymmetric model is always well-behaved the nonsupersymmetric model is unitary only over a small parameter range. We offer some speculations on the origin of strings from the higher spins.

Spectral Filtering Induced by Non-Hermitian Evolution with Balanced Gain and Loss: Enhancing Quantum Chaos

The dynamical signatures of quantum chaos in an isolated system are captured by the spectral form factor, which exhibits as a function of time a dip, a ramp, and a plateau, with the ramp being governed by the correlations in the level spacing distribution. While decoherence generally suppresses these dynamical signatures, the nonlinear non-Hermitian evolution with balanced gain and loss (BGL) in an energy-dephasing scenario can enhance manifestations of quantum chaos. In the Sachdev-Ye-Kitaev model and random matrix Hamiltonians, BGL increases the span of the ramp, lowering the dip as well as the value of the plateau, providing an experimentally realizable physical mechanism for spectral filtering. The chaos enhancement due to BGL is optimal over a family of filter functions that can be engineered with fluctuating Hamiltonians.

Quantum Charging Advantage Cannot Be Extensive without Global Operations

Quantum batteries are devices made from quantum states, which store and release energy in a fast and efficient manner, thus offering numerous possibilities in future technological applications. They offer a significant charging speedup when compared to classical batteries, due to the possibility of using entangling charging operations. We show that the maximal speedup that can be achieved is extensive in the number of cells, thus offering at most quadratic scaling in the charging power over the classically achievable linear scaling. To reach such a scaling, a global charging protocol, charging all the cells collectively, needs to be employed. This concludes the quest on the limits of charging power of quantum batteries and adds to other results in which quantum methods are known to provide at most quadratic scaling over their classical counterparts.

Non-Fermi liquid phase and linear-in-temperature scattering rate in overdoped two-dimensional Hubbard model

SignificanceMost metals display an electron-scattering rate [Formula: see text] that follows [Formula: see text] at low temperatures, as prescribed by Fermi liquid theory. But there are important exceptions. One of the most prominent examples is the "strange" metal regime in overdoped cuprate supercondcutors, which exhibits a linear T dependence of the scattering rate [Formula: see text] that reaches a putative Planckian limit. Here, using cutting-edge computational approaches, we show that T-linear scattering rate can emerge from the overdoped Hubbard model at low temperatures. Our results agree with cuprate experiments in various aspects but challenge the Planckian limit. Finally, by identifying antiferromagnetic fluctuations as the physical origin of the T-linear scattering rate, we discover the microscopic mechanism of strange metallicity in cuprates.

Sachdev-Ye-Kitaev Circuits for Braiding and Charging Majorana Zero Modes

The Sachdev-Ye-Kitaev (SYK) model is an all-to-all interacting Majorana fermion model for many-body quantum chaos and the holographic correspondence. Here we construct fermionic all-to-all Floquet quantum circuits of random four-body gates designed to capture key features of SYK dynamics. Our circuits can be built using local ingredients in Majorana devices, namely, charging-mediated interactions and braiding Majorana zero modes. This offers an analog-digital route to SYK quantum simulations that reconciles all-to-all interactions with the topological protection of Majorana zero modes, a key feature missing in existing proposals for analog SYK simulation. We also describe how dynamical, including out-of-time-ordered, correlation functions can be measured in such analog-digital implementations by employing foreseen capabilities in Majorana devices.

Quantum information in holographic duality

We give a pedagogical review of how concepts from quantum information theory build up the gravitational side of the anti-de Sitter/conformal field theory correspondence. The review is self-contained in that it only presupposes knowledge of quantum mechanics and general relativity; other tools-including holographic duality itself-are introduced in the text. We have aimed to give researchers interested in entering this field a working knowledge sufficient for initiating original projects. The review begins with the laws of black hole thermodynamics, which form the basis of this subject, then introduces the Ryu-Takayanagi proposal, the Jafferis-Lewkowycz-Maldacena-Suh (JLMS) relation, and subregion duality. We discuss tensor networks as a visualization tool and analyze various network architectures in detail. Next, several modern concepts and techniques are discussed: Rényi entropies and the replica trick, differential entropy and kinematic space, modular Berry phases, modular minimal entropy, entanglement wedge cross-sections, bit threads, and others. We discuss the extent to which bulk geometries are fixed by boundary entanglement entropies, and analyze the relations such as the monogamy of mutual information, which boundary entanglement entropies must obey if a state has a semiclassical bulk dual. We close with a discussion of black holes, including holographic complexity, firewalls and the black hole information paradox, islands, and replica wormholes.

Quantum simulation of operator spreading in the chaotic Ising model

There is great interest in using near-term quantum computers to simulate and study foundational problems in quantum mechanics and quantum information science, such as the scrambling measured by an out-of-time-ordered correlator (OTOC). Here we use an IBM Q processor, quantum error mitigation, and weaved Trotter simulation to study high-resolution operator spreading in a four-spin Ising model as a function of space, time, and integrability. Reaching four spins while retaining high circuit fidelity is made possible by the use of a physically motivated fixed-node variant of the OTOC, allowing scrambling to be estimated without overhead. We find clear signatures of a ballistic operator spreading in a chaotic regime, as well as operator localization in an integrable regime. The techniques developed and demonstrated here open up the possibility of using cloud-based quantum computers to study and visualize scrambling phenomena, as well as quantum information dynamics more generally.