Nonequilibrium Steady State Generated by a Moving Defect: The Supersonic Threshold

Transport and Entanglement across Integrable Impurities from Generalized Hydrodynamics

Quantum impurity models (QIMs) are ubiquitous throughout physics. As simplified toy models they provide crucial insights for understanding more complicated strongly correlated systems, while in their own right are accurate descriptions of many experimental platforms. In equilibrium, their physics is well understood and have proven a testing ground for many powerful theoretical tools, both numerical and analytical, in use today. Their nonequilibrium physics is much less studied and understood. However, the recent advancements in nonequilibrium integrable quantum systems through the development of generalized hydrodynamics (GHD) coupled with the fact that many archetypal QIMs are in fact integrable presents an enticing opportunity to enhance our understanding of these systems. We take a step towards this by expanding the framework of GHD to incorporate integrable interacting QIMs. We present a set of Bethe-Boltzmann type equations which incorporate the effects of impurity scattering and discuss the new aspects which include entropy production. These impurity GHD equations are then used to study a bipartioning quench wherein a relevant backscattering impurity is included at the location of the bipartition. The density and current profiles are studied as a function of the impurity strength and expressions for the entanglement entropy and full counting statistics are derived.

Global Quenches after Localized Perturbations

We investigate the effect of a single spin flip preceding a global quench between translationally invariant local Hamiltonians in spin-1/2 chains. The effect of the localized perturbation does not fade away however large the distance from the perturbation is. In particular, translational invariance is not restored and the infinite-time limit depends on whether the spin was flipped or not. We argue that this phenomenon is more general than the particular example considered and we conjecture that it is triggered by topological properties, specifically, the existence of "semilocal charges."

Ballistic transport and boundary resistances in inhomogeneous quantum spin chains

Transport phenomena are central to physics, and transport in the many-body and fully-quantum regime is attracting an increasing amount of attention. It has been recently revealed that some quantum spin chains support ballistic transport of excitations at all energies. However, when joining two semi-infinite ballistic parts, such as the XX and XXZ spin-1/2 models, our understanding suddenly becomes less established. Employing a matrix-product-state ansatz of the wavefunction, we study the relaxation dynamics in this latter case. Here we show that it takes place inside a light cone, within which two qualitatively different regions coexist: an inner one with a strong tendency towards thermalization, and an outer one supporting ballistic transport. We comment on the possibility that even at infinite time the system supports stationary currents and displays a non-zero Kapitza boundary resistance. Our study paves the way to the analysis of the interplay between transport, integrability, and local defects.

Generalized Hydrodynamics with Space-Time Inhomogeneous Interactions

We provide a new hydrodynamic framework to describe out-of-equilibrium integrable systems with space-time inhomogeneous interactions. Our result builds up on the recently introduced generalized hydrodynamics (GHD). The method allows us to analytically describe the dynamics during generic space-time-dependent smooth modulations of the interactions. As a proof of concept, we study experimentally motivated interaction quenches in the trapped interacting Bose gas, which cannot be treated with current analytical or numerical methods. We also benchmark our results in the XXZ spin chain and in the classical sinh-Gordon model.

Integrability-Protected Adiabatic Reversibility in Quantum Spin Chains

We consider the out-of-equilibrium dynamics of the Heisenberg anisotropic quantum spin-1/2 chain threaded by a time-dependent magnetic flux. In the spirit of the recently developed generalized hydrodynamics (GHD), we exploit the integrability of the model for any flux values to derive an exact description of the dynamics in the limit of slowly varying flux: the state of the system is described at any time by a time-dependent generalized Gibbs ensemble. Two dynamical regimes emerge according to the value of the anisotropy Δ. For |Δ|>1, reversibility is preserved: the initial state is always recovered whenever the flux is brought back to zero. On the contrary, for |Δ|<1, instabilities of quasiparticles produce irreversible dynamics as confirmed by the dramatic growth of entanglement entropy. In this regime, the standard GHD description becomes incomplete and we complement it via a maximum entropy production principle. We test our predictions against numerical simulations finding excellent agreement.

Universal Broadening of the Light Cone in Low-Temperature Transport

We consider the low-temperature transport properties of critical one-dimensional systems that can be described, at equilibrium, by a Luttinger liquid. We focus on the prototypical setting where two semi-infinite chains are prepared in two thermal states at small but different temperatures and suddenly joined together. At large distances x and times t, conformal field theory characterizes the energy transport in terms of a single light cone spreading at the sound velocity v. Energy density and current take different constant values inside the light cone, on its left, and on its right, resulting in a three-step form of the corresponding profiles as a function of ζ=x/t. Here, using a nonlinear Luttinger liquid description, we show that for generic observables this picture is spoiled as soon as a nonlinearity in the spectrum is present. In correspondence of the transition points x/t=±v, a novel universal region emerges at infinite times, whose width is proportional to the temperatures on the two sides. In this region, expectation values have a different temperature dependence and show smooth peaks as a function of ζ. We explicitly compute the universal function describing such peaks. In the specific case of interacting integrable models, our predictions are analytically recovered by the generalized hydrodynamic approach.