Exact Universal Bounds on Quantum Dynamics and Fast Scrambling

Quantum speed limits such as the Mandelstam-Tamm or Margolus-Levitin bounds offer a quantitative formulation of the energy-time uncertainty principle that constrains dynamics over short times. We show that the spectral form factor, a central quantity in quantum chaos, sets a universal state-independent bound on the quantum dynamics of a complete set of initial states over arbitrarily long times, which is tighter than the corresponding state-independent bounds set by known speed limits. This bound further generalizes naturally to the real-time dynamics of time-dependent or dissipative systems where no energy spectrum exists. We use this result to constrain the scrambling of information in interacting many-body systems. For Hamiltonian systems, we show that the fundamental question of the fastest possible scrambling time-without any restrictions on the structure of interactions-maps to a purely mathematical property of the density of states involving the non-negativity of Fourier transforms. We illustrate these bounds in the Sachdev-Ye-Kitaev model, where we show that despite its "maximally chaotic" nature, the sustained scrambling of sufficiently large fermion subsystems via entanglement generation requires an exponentially long time in the subsystem size.

Strongly correlated electron-photon systems

An important goal of modern condensed-matter physics involves the search for states of matter with emergent properties and desirable functionalities. Although the tools for material design remain relatively limited, notable advances have been recently achieved by controlling interactions at heterointerfaces, precise alignment of low-dimensional materials and the use of extreme pressures. Here we highlight a paradigm based on controlling light-matter interactions, which provides a way to manipulate and synthesize strongly correlated quantum matter. We consider the case in which both electron-electron and electron-photon interactions are strong and give rise to a variety of phenomena. Photon-mediated superconductivity, cavity fractional quantum Hall physics and optically driven topological phenomena in low dimensions are among the frontiers discussed in this Perspective, which highlights a field that we term here 'strongly correlated electron-photon science'.

Chiral Anomaly in Interacting Condensed Matter Systems

The chiral anomaly is a fundamental quantum mechanical phenomenon which is of great importance to both particle physics and condensed matter physics alike. In the context of QED, it manifests as the breaking of chiral symmetry in the presence of electromagnetic fields. It is also known that anomalous chiral symmetry breaking can occur through interactions alone, as is the case for interacting one-dimensional systems. In this Letter, we investigate the interplay between these two modes of anomalous chiral symmetry breaking in the context of interacting Weyl semimetals. Using Fujikawa's path integral method, we show that the chiral charge continuity equation is modified by the presence of interactions which can be viewed as including the effect of the electric and magnetic fields generated by the interacting quantum matter. This can be understood further using dimensional reduction and a Luttinger liquid description of the lowest Landau level. These effects manifest themselves in the nonlinear response of the system. In particular, we find an interaction-dependent density response due to a change in the magnetic field as well as a contribution to the nonequilibrium and inhomogeneous anomalous Hall response while preserving its equilibrium value.

Many-Body Level Statistics of Single-Particle Quantum Chaos

We consider a noninteracting many-fermion system populating levels of a unitary random matrix ensemble (equivalent to the q=2 complex Sachdev-Ye-Kitaev model)-a generic model of single-particle quantum chaos. We study the corresponding many-particle level statistics by calculating the spectral form factor analytically using algebraic methods of random matrix theory, and match it with an exact numerical simulation. Despite the integrability of the theory, the many-body spectral rigidity is found to have a surprisingly rich landscape. In particular, we find a residual repulsion of distant many-body levels stemming from single-particle chaos, together with islands of level attraction. These results are encoded in an exponential ramp in the spectral form factor, which we show to be a universal feature of nonergodic many-fermion systems embedded in a chaotic medium.

Early-Time Exponential Instabilities in Nonchaotic Quantum Systems

The majority of classical dynamical systems are chaotic and exhibit the butterfly effect: a minute change in initial conditions has exponentially large effects later on. But this phenomenon is difficult to reconcile with quantum mechanics. One of the main goals in the field of quantum chaos is to establish a correspondence between the dynamics of classical chaotic systems and their quantum counterparts. In isolated systems in the absence of decoherence, there is such a correspondence in dynamics, but it usually persists only over a short time window, after which quantum interference washes out classical chaos. We demonstrate that quantum mechanics can also play the opposite role and generate exponential instabilities in classically nonchaotic systems within this early-time window. Our calculations employ the out-of-time-ordered correlator (OTOC)-a diagnostic that reduces to the Lyapunov exponent in the classical limit but is well defined for general quantum systems. We show that certain classically nonchaotic models, such as polygonal billiards, demonstrate a Lyapunov-like exponential growth of the OTOC at early times with Planck's-constant-dependent rates. This behavior is sharply contrasted with the slow early-time growth of the analog of the OTOC in the systems' classical counterparts. These results suggest that classical-to-quantum correspondence in dynamics is violated in the OTOC even before quantum interference develops.

Photon-Mediated Peierls Transition of a 1D Gas in a Multimode Optical Cavity

The Peierls instability toward a charge density wave is a canonical example of phonon-driven strongly correlated physics and is intimately related to topological quantum matter and exotic superconductivity. We propose a method for realizing an analogous photon-mediated Peierls transition, using a system of one-dimensional tubes of interacting Bose or Fermi atoms trapped inside a multimode confocal cavity. Pumping the cavity transversely engineers a cavity-mediated metal-to-insulator transition in the atomic system. For strongly interacting bosons in the Tonks-Girardeau limit, this transition can be understood (through fermionization) as being the Peierls instability. We extend the calculation to finite values of the interaction strength and derive analytic expressions for both the cavity field and mass gap. They display nontrivial power law dependence on the dimensionless matter-light coupling.

Many-Body Dynamical Localization in a Kicked Lieb-Liniger Gas

The kicked rotor system is a textbook example of how classical and quantum dynamics can drastically differ. The energy of a classical particle confined to a ring and kicked periodically will increase linearly in time whereas in the quantum version the energy saturates after a finite number of kicks. The quantum system undergoes Anderson localization in angular-momentum space. Conventional wisdom says that in a many-particle system with short-range interactions the localization will be destroyed due to the coupling of widely separated momentum states. Here we provide evidence that for an interacting one-dimensional Bose gas, the Lieb-Liniger model, the dynamical localization can persist at least for an unexpectedly long time.

Electron Induced Massive Dynamics of Magnetic Domain Walls

We study the dynamics of domain walls (DWs) in a metallic, ferromagnetic nanowire, focusing on inertial effects on the DW due to interaction with a conduction electron bath. We develop a Keldysh collective coordinate technique to describe the effect of conduction electrons on rigid magnetic structures. The effective Lagrangian and Langevin equations of motion for a DW are derived microscopically, including the full response kernel which is nonlocal in time. The DW dynamics is described by two collective degrees of freedom: position and tilt-angle. The coupled Langevin equations therefore involve two correlated noise sources, leading to a generalized fluctuation-dissipation theorem (FDT). The DW response kernel due to electrons contains two parts: one related to dissipation via FDT, and another reactive part. We prove that the latter term leads to a mass for both degrees of freedom, even though the intrinsic bare mass is zero. The electron-induced mass is present even in a clean system without pinning or specifically engineered potentials. The resulting equations of motion contain rich dynamical solutions and point toward a way to control domain wall motion in metals via the electronic system properties. We discuss two observable consequences of the mass, hysteresis in the DW dynamics and resonant response to ac current.

Dynamo Effect and Turbulence in Hydrodynamic Weyl Metals

The dynamo effect is a class of macroscopic phenomena responsible for generating and maintaining magnetic fields in astrophysical bodies. It hinges on the hydrodynamic three-dimensional motion of conducting gases and plasmas that achieve high hydrodynamic and/or magnetic Reynolds numbers due to the large length scales involved. The existing laboratory experiments modeling dynamos are challenging and involve large apparatuses containing conducting fluids subject to fast helical flows. Here we propose that electronic solid-state materials-in particular, hydrodynamic metals-may serve as an alternative platform to observe some aspects of the dynamo effect. Motivated by recent experimental developments, this Letter focuses on hydrodynamic Weyl semimetals, where the dominant scattering mechanism is due to interactions. We derive Navier-Stokes equations along with equations of magnetohydrodynamics that describe the transport of a Weyl electron-hole plasma appropriate in this regime. We estimate the hydrodynamic and magnetic Reynolds numbers for this system. The latter is a key figure of merit of the dynamo mechanism. We show that it can be relatively large to enable observation of the dynamo-induced magnetic field bootstrap in an experiment. Finally, we generalize the simplest dynamo instability model-the Ponomarenko dynamo-to the case of a hydrodynamic Weyl semimetal and show that the chiral anomaly term reduces the threshold magnetic Reynolds number for the dynamo instability.

Out-of-time-order correlators in finite open systems

We study out-of-time-order correlators (OTOCs) of the form 〈 A ^ ( t ) B ^ ( 0 ) C ^ ( t ) D ^ ( 0 ) 〉 for a quantum system weakly coupled to a dissipative environment. Such an open system may serve as a model of, e.g., a small region in a disordered interacting medium coupled to the rest of this medium considered as an environment. We demonstrate that for a system with discrete energy levels the OTOC saturates exponentially ∝Σa i e -t/τi + const to a constant value at t → ∞, in contrast with quantum-chaotic systems which exhibit exponential growth of OTOCs. Focusing on the case of a two-level system, we calculate microscopically the decay times τ i and the value of the saturation constant. Because some OTOCs are immune to dephasing processes and some are not, such correlators may decay on two sets of parametrically different time scales related to inelastic transitions between the system levels and to pure dephasing processes, respectively. In the case of a classical environment, the evolution of the OTOC can be mapped onto the evolution of the density matrix of two systems coupled to the same dissipative environment.

Kinetic theory of dark solitons with tunable friction

We study controllable friction in a system consisting of a dark soliton in a one-dimensional Bose-Einstein condensate coupled to a noninteracting Fermi gas. The fermions act as impurity atoms, not part of the original condensate, that scatter off of the soliton. We study semiclassical dynamics of the dark soliton, a particlelike object with negative mass, and calculate its friction coefficient. Surprisingly, it depends periodically on the ratio of interspecies (impurity-condensate) to intraspecies (condensate-condensate) interaction strengths. By tuning this ratio, one can access a regime where the friction coefficient vanishes. We develop a general theory of stochastic dynamics for negative-mass objects and find that their dynamics are drastically different from their positive-mass counterparts: they do not undergo Brownian motion. From the exact phase-space probability distribution function (i.e., in position and velocity), we find that both the trajectory and lifetime of the soliton are altered by friction, and the soliton can undergo Brownian motion only in the presence of friction and a confining potential. These results agree qualitatively with experimental observations by Aycock et al. [Proc. Natl. Acad. Sci. USA 114, 2503 (2017)] in a similar system with bosonic impurity scatterers.

Lyapunov Exponent and Out-of-Time-Ordered Correlator's Growth Rate in a Chaotic System

It was proposed recently that the out-of-time-ordered four-point correlator (OTOC) may serve as a useful characteristic of quantum-chaotic behavior, because, in the semiclassical limit ℏ→0, its rate of exponential growth resembles the classical Lyapunov exponent. Here, we calculate the four-point correlator C(t) for the classical and quantum kicked rotor-a textbook driven chaotic system-and compare its growth rate at initial times with the standard definition of the classical Lyapunov exponent. Using both quantum and classical arguments, we show that the OTOC's growth rate and the Lyapunov exponent are, in general, distinct quantities, corresponding to the logarithm of the phase-space averaged divergence rate of classical trajectories and to the phase-space average of the logarithm, respectively. The difference appears to be more pronounced in the regime of low kicking strength K, where no classical chaos exists globally. In this case, the Lyapunov exponent quickly decreases as K→0, while the OTOC's growth rate may decrease much slower, showing a higher sensitivity to small chaotic islands in the phase space. We also show that the quantum correlator as a function of time exhibits a clear singularity at the Ehrenfest time t_{E}: transitioning from a time-independent value of t^{-1}lnC(t) at t<t_{E} to its monotonic decrease with time at t>t_{E}. We note that the underlying physics here is the same as in the theory of weak (dynamical) localization [Aleiner and Larkin, Phys. Rev. B 54, 14423 (1996)PRBMDO0163-182910.1103/PhysRevB.54.14423; Tian, Kamenev, and Larkin, Phys. Rev. Lett. 93, 124101 (2004)PRLTAO0031-900710.1103/PhysRevLett.93.124101] and is due to a delay in the onset of quantum interference effects, which occur sharply at a time of the order of the Ehrenfest time.

Amperean Pairing at the Surface of Topological Insulators

The surface of a 3D topological insulator is described by a helical electron state with the electron's spin and momentum locked together. We show that in the presence of ferromagnetic fluctuations the surface of a topological insulator is unstable towards a superconducting state with unusual pairing, dubbed Amperean pairing. The key idea is that the dynamical fluctuations of a ferromagnetic layer deposited on the surface of a topological insulator couple to the electrons as gauge fields. The transverse components of the magnetic gauge fields are unscreened and can mediate an effective interaction between electrons. There is an attractive interaction between electrons with momenta in the same direction which makes the pairing to be of Amperean type. We show that this attractive interaction leads to a p-wave pairing instability of the Fermi surface in the Cooper channel.

Non-Markovian Quantum Friction of Bright Solitons in Superfluids

We explore the quantum dynamics of a bright matter-wave soliton in a quasi-one-dimensional bosonic superfluid with attractive interactions. Specifically, we focus on the dissipative forces experienced by the soliton due to its interaction with Bogoliubov excitations. Using the collective coordinate approach and the Keldysh formalism, a Langevin equation of motion for the soliton is derived from first principles. The equation contains a stochastic Langevin force (associated with quantum noise) and a nonlocal in time dissipative force, which appears due to inelastic scattering of Bogoliubov quasiparticles off of the moving soliton. It is shown that Ohmic friction (i.e., a term proportional to the soliton's velocity) is absent in the integrable setup. However, the Markovian approximation gives rise to the Abraham-Lorentz force (i.e., a term proportional to the derivative of the soliton's acceleration), which is known from classical electrodynamics of a charged particle interacting with its own radiation. These Abraham-Lorentz equations famously contain a fundamental causality paradox, where the soliton (particle) interacts with excitations (radiation) originating from future events. We show, however, that the causality paradox is an artifact of the Markovian approximation, and our exact non-Markovian dissipative equations give rise to physical trajectories. We argue that the quantum friction discussed here should be observable in current quantum gas experiments.

Radio Frequency Tunable Oscillator Device Based on a SmB_{6} Microcrystal

Radio frequency tunable oscillators are vital electronic components for signal generation, characterization, and processing. They are often constructed with a resonant circuit and a "negative" resistor, such as a Gunn diode, involving complex structure and large footprints. Here we report that a piece of SmB_{6}, 100  μm in size, works as a current-controlled oscillator in the 30 MHz frequency range. SmB_{6} is a strongly correlated Kondo insulator that was recently found to have a robust surface state likely to be protected by the topology of its electronics structure. We exploit its nonlinear dynamics, and demonstrate large ac voltage outputs with frequencies from 20 Hz to 30 MHz by adjusting a small dc bias current. The behaviors of these oscillators agree well with a theoretical model describing the thermal and electronic dynamics of coupled surface and bulk states. With reduced crystal size we anticipate the device to work at higher frequencies, even in the THz regime. This type of oscillator might be realized in other materials with a metallic surface and a semiconducting bulk.

Anomalous Coulomb Drag in Electron-Hole Bilayers due to the Formation of Excitons

Several recent experiments have reported an anomalous temperature dependence of the Coulomb drag effect in electron-hole bilayers. Motivated by these puzzling data, we study theoretically a low-density electron-hole bilayer, where electrons and holes avoid quantum degeneracy by forming excitons. We describe the ionization-recombination crossover between the electron-hole plasma and exciton gas and calculate both the intralayer and drag resistivity as a function of temperature. The latter exhibits a minimum followed by a sharp upturn at low temperatures, in qualitative agreement with the experimental observations [see, e.g., J. A. Seamons et al., Phys. Rev. Lett. 102, 026804 (2009)]. Importantly, the drag resistivity in the proposed scenario is found to be rather insensitive to a mismatch in electron and hole concentrations, in sharp contrast to the scenario of electron-hole Cooper pairing.

Gigantic surface lifetime of an intrinsic topological insulator

The interaction between light and novel two-dimensional electronic states holds promise to realize new fundamental physics and optical devices. Here, we use pump-probe photoemission spectroscopy to study the optically excited Dirac surface states in the bulk-insulating topological insulator Bi_{2}Te_{2}Se and reveal optical properties that are in sharp contrast to those of bulk-metallic topological insulators. We observe a gigantic optical lifetime exceeding 4  μs (1  μs=10^{-6}  s) for the surface states in Bi_{2}Te_{2}Se, whereas the lifetime in most topological insulators, such as Bi_{2}Se_{3}, has been limited to a few picoseconds (1  ps=10^{-12}  s). Moreover, we discover a surface photovoltage, a shift of the chemical potential of the Dirac surface states, as large as 100 mV. Our results demonstrate a rare platform to study charge excitation and relaxation in energy and momentum space in a two-dimensional system.

Stoner ferromagnetism in a thermal pseudospin-1/2 Bose gas

We compute the finite-temperature phase diagram of a pseudospin-1/2 Bose gas with contact interactions, using two complementary methods: the random-phase approximation and self-consistent Hartree-Fock theory. We show that the spin-dependent interactions, which break the (pseudo-) spin-rotational symmetry of the Hamiltonian, generally lead to the appearance of a magnetically ordered phase at temperatures above the superfluid transition. In three dimensions, we predict a normal easy-axis (easy-plane) ferromagnet for sufficiently strong repulsive (attractive) interspecies interactions, respectively. The normal easy-axis ferromagnet is the bosonic analog of Stoner ferromagnetism known in electronic systems. For the case of interspecies attraction, we also discuss the possibility of a bosonic analog of the Cooper-paired phase. This state is shown to significantly lose in energy to the transverse ferromagnet in three dimensions, but is more energetically competitive in lower dimensions. Extending our calculations to a spin-orbit-coupled Bose gas with equal Rashba and Dresselhaus-type couplings (as recently realized in experiment), we investigate the possibility of stripe ordering in the normal phase. Within our approximations, however, we do not find an instability towards stripe formation, suggesting that the stripe order melts below the condensation temperature, which is consistent with the experimental observations of Ji et al. [Ji et al., Nat. Phys. 10, 314 (2014)].

Interaction-tuned dynamical transitions in a Rashba spin-orbit-coupled Fermi gas

We consider the time evolution of the magnetization in a Rashba spin-orbit coupled Fermi gas, starting from a fully polarized initial state. We model the dynamics using a Boltzmann equation, which we solve in the Hartree-Fock approximation. The resulting nonlinear system of equations gives rise to three distinct dynamical regimes with qualitatively different asymptotic behaviors of the magnetization at long times. The distinct regimes and the transitions between them are controlled by the ratio of interaction and spin-orbit coupling strength λ: for small λ, the magnetization decays to zero. For intermediate λ, it displays undamped oscillations about zero, and for large λ, a partially magnetized state is dynamically stabilized. The dynamics we find is a spin analog of interaction induced self-trapping in double-well Bose Einstein condensates. The predicted phenomena can be realized in trapped Fermi gases with synthetic spin-orbit interactions.

Magnetoresistance of an Anderson insulator of bosons

We study the magnetoresistance of two-dimensional bosonic Anderson insulators. We describe the change in spatial decay of localized excitations in response to a magnetic field, which is given by an interference sum over alternative tunneling trajectories. The excitations become more localized with increasing field (in sharp contrast to generic fermionic excitations which get weakly delocalized): the localization length ξ(B) is found to change as ξ(-1)(B)-ξ(-1)(0)~B(4/5). The quantum interference problem maps onto the classical statistical mechanics of directed polymers in random media (DPRM). We explain the observed scaling using a simplified droplet model which incorporates the nontrivial DPRM exponents. Our results have implications for a variety of experiments on magnetic-field-tuned superconductor-to-insulator transitions observed in disordered films, granular superconductors, and Josephson junction arrays, as well as for cold atoms in artificial gauge fields.

SU(3) spin-orbit coupling in systems of ultracold atoms

Motivated by the recent experimental success in realizing synthetic spin-orbit coupling in ultracold atomic systems, we consider N-component atoms coupled to a non-Abelian SU(N) gauge field. More specifically, we focus on the case, referred to here as "SU(3) spin-orbit-coupling," where the internal states of three-component atoms are coupled to their momenta via a matrix structure that involves the Gell-Mann matrices (in contrast to the Pauli matrices in conventional SU(2) spin-orbit-coupled systems). It is shown that the SU(3) spin-orbit-coupling gives rise to qualitatively different phenomena and in particular we find that even a homogeneous SU(3) field on a simple square lattice enables a topologically nontrivial state to exist, while such SU(2) systems always have trivial topology. In deriving this result, we first establish an equivalence between the Hofstadter model with a 1/N Abelian flux per plaquette and a homogeneous SU(N) non-Abelian model. The former is known to have a topological spectrum for N>2, which is thus inherited by the latter. It is explicitly verified by an exact calculation for N=3, where we develop and use a new algebraic method to calculate topological indices in the SU(3) case. Finally, we consider a strip geometry and establish the existence of three gapless edge states-the hallmark feature of such an SU(3) topological insulator.

Exotic quantum spin models in spin-orbit-coupled Mott insulators

We study cold atoms in an optical lattice with synthetic spin-orbit coupling in the Mott-insulator regime. We calculate the parameters of the corresponding tight-binding model using Peierls substitution and "localized Wannier states method" and derive the low-energy spin Hamiltonian for bosons and fermions. The spin Hamiltonian is a combination of Heisenberg model, quantum compass model and Dzyaloshinskii-Moriya interactions and it has a rich classical phase diagram with collinear, spiral and vortex phases. We discuss the state of the art of experiments to realize and detect magnetic orderings in strongly correlated optical lattices.

Kaleidoscope of exotic quantum phases in a frustrated XY model

The existence of quantum spin liquids was first conjectured by Pomeranchuk some 70 years ago, who argued that frustration in simple antiferromagnetic theories could result in a Fermi-liquid-like state for spinon excitations. Here we show that a simple quantum spin model on a honeycomb lattice hosts the long sought for Bose metal with a clearly identifiable Bose surface. The complete phase diagram of the model is determined via exact diagonalization and is shown to include four distinct phases separated by three quantum phase transitions.

Breakdown of the coherent state path integral: two simple examples

We show how the time-continuous coherent state path integral breaks down for both the single-site Bose-Hubbard model and the spin-path integral. Specifically, when the Hamiltonian is quadratic in a generator of the algebra used to construct coherent states, the path integral fails to produce correct results following from an operator approach. As suggested by previous authors, we note that the problems do not arise in the time-discretized version of the path integral.

Topological Kondo insulators

Kondo insulators are a particularly simple type of heavy electron material, where a filled band of heavy quasiparticles gives rise to a narrow band insulator. Starting with the Anderson lattice Hamiltonian, we develop a topological classification of emergent band structures for Kondo insulators and show that these materials may host three-dimensional topological insulating phases. We propose a general and practical prescription of calculating the Z(2) topological indices for various lattice structures. Experimental implications of the topological Kondo insulating behavior are discussed.

Splitting of Majorana-fermion modes due to intervortex tunneling in a p(x) + ip(y) superconductor

We consider a two-dimensional (p(x) + ip(y)) superconductor in the presence of multiple vortices, which support zero-energy Majorana-fermion states in their cores. Intervortex tunnelings of the Majorana fermions lift the topological state degeneracy. Using the Bogoliubov-de Gennes equation, we calculate splitting of the zero-energy modes due to these tunneling events. We also discuss superconducting fluctuations and, in particular, their effect on the energy splitting.

Giant Nernst effect due to fluctuating cooper pairs in superconductors

A theory of the fluctuation-induced Nernst effect is developed for a two-dimensional superconductor in a perpendicular magnetic field. First, we derive a simple phenomenological formula for the Nernst coefficient, which naturally explains the giant Nernst signal due to fluctuating Cooper pairs. The latter signal is shown to be large even far from the transition and may exceed by orders of magnitude the Fermi liquid terms. We also present a complete microscopic calculation of the Nernst coefficient for arbitrary magnetic fields and temperatures, which is based on the Matsubara-Kubo formalism. It is shown that the magnitude and the behavior of the Nernst signal observed experimentally in disordered superconducting films can be well understood on the basis of superconducting fluctuation theory.

Dissipation-driven quantum phase transition in superconductor-graphene systems

We show that a system of Josephson junctions coupled via low-resistance tunneling contacts to graphene substrate(s) may effectively operate as a current switching device. The effect is based on the dissipation-driven superconductor-to-insulator quantum phase transition, which happens due to the interplay of the Josephson effect and Coulomb blockade. Coupling to a graphene substrate with gapless excitations further enhances charge fluctuations favoring superconductivity. The effect is shown to scale exponentially with the Fermi energy in graphene, which can be controlled by the gate voltage. We develop a theory that quantitatively describes the quantum phase transition in a two-dimensional Josephson junction array, but it is expected to provide a reliable qualitative description for one-dimensional systems as well.

Effective masses in a strongly anisotropic fermi liquid

Motivated by the recent experimental observation of quantum oscillations in the underdoped cuprates, we study the cyclotron and infrared Hall effective masses in an anisotropic Fermi liquid characterized by an angle-dependent quasiparticle residue Z_{q}. Our primary motivation is to explain the relatively large value of the cyclotron mass observed experimentally and its relation with the effective Hall mass. Using a phenomenological model of an anisotropic Fermi liquid, we find that the cyclotron mass is enhanced by a factor 1/Z_{q}, while the effective Hall mass is proportional to Z_{q}/Z_{q};{2}, where cdots, three dots, centered implies an averaging over the Fermi surface. If the Z-factor becomes small in some part of the Fermi surface (e.g., in the case of a Fermi arc), the cyclotron mass is enhanced sharply while the infrared Hall mass may remain small.

Nonperturbative microscopic theory of superconducting fluctuations near a quantum critical point

We consider an anisotropic gap superconductor in the vicinity of the disorder-driven quantum critical point. Starting with the BCS Hamiltonian, we derive the Ginzburg-Landau action, which is a critical theory with the dynamic critical exponent, z=2. This allows us to use the parquet method to calculate the nonperturbative effect of quantum superconducting fluctuations on thermodynamics. We derive a general expression for the fluctuation magnetic susceptibility, which exhibits a crossover from the logarithmic dependence, chi proportional, variantlndeltan, valid beyond the Ginzburg region to chi proportional, variantln(1/5)deltan valid in the immediate vicinity of the transition (where deltan is the deviation from the critical disorder concentration). These nonperturbative results may describe the quantum critical behavior of overdoped high-temperature cuprates, disordered p-wave superconductors, and conventional superconducting films with magnetic impurities.

Spin-triplet pairing instability of the spinon fermi surface in a U(1) spin liquid

Recent experiments on the organic compound kappa-(ET)2Cu2(CN)3 have provided a promising example of a two-dimensional spin liquid state. This phase is described by a two-dimensional spinon Fermi sea coupled to a U(1) gauge field. We study Kohn-Luttinger-like pairing instabilities of the spinon Fermi surface due to singular interaction processes with twice-the-Fermi-momentum transfer. We find that under certain circumstances the pairing instability occurs in odd-orbital-angular momentum or spin-triplet channels. Implications to experiments are discussed.

Nonequilibrium spin dynamics in a trapped fermi gas with effective spin-orbit interactions

We consider a trapped atomic system in the presence of spatially varying laser fields. The laser-atom interaction generates a pseudospin degree of freedom (referred to simply as spin) and leads to an effective spin-orbit coupling for the fermions in the trap. Reflections of the fermions from the trap boundaries provide a physical mechanism for effective momentum relaxation and nontrivial spin dynamics due to the emergent spin-orbit coupling. We explicitly consider evolution of an initially spin-polarized Fermi gas in a two-dimensional harmonic trap and derive nonequilibrium behavior of the spin polarization. It shows periodic echoes with a frequency equal to the harmonic trapping frequency. Perturbations, such as an asymmetry of the trap, lead to the suppression of the spin echo amplitudes. We discuss a possible experimental setup to observe spin dynamics and provide numerical estimates of relevant parameters.