Integrability-Protected Adiabatic Reversibility in Quantum Spin Chains

Hydrodynamic nonlinear response of interacting integrable systems

We develop a formalism for computing the nonlinear response of interacting integrable systems. Our results are asymptotically exact in the hydrodynamic limit where perturbing fields vary sufficiently slowly in space and time. We show that spatially resolved nonlinear response distinguishes interacting integrable systems from noninteracting ones, exemplifying this for the Lieb-Liniger gas. We give a prescription for computing finite-temperature Drude weights of arbitrary order, which is in excellent agreement with numerical evaluation of the third-order response of the XXZ spin chain. We identify intrinsically nonperturbative regimes of the nonlinear response of integrable systems.

Thermalization of a Trapped One-Dimensional Bose Gas via Diffusion

For a decade the fate of a one-dimensional gas of interacting bosons in an external trapping potential remained mysterious. We here show that whenever the underlying integrability of the gas is broken by the presence of the external potential, the inevitable diffusive rearrangements between the quasiparticles, quantified by the diffusion constants of the gas, eventually lead the system to thermalize at late times. We show that the full thermalizing dynamics can be described by the generalized hydrodynamics with diffusion and force terms, and we compare these predictions to numerical simulations. Finally, we provide an explanation for the slow thermalization rates observed in numerical and experimental settings: the hydrodynamics of integrable models is characterized by a continuity of modes, which can have arbitrarily small diffusion coefficients. As a consequence, the approach to thermalization can display prethermal plateau and relaxation dynamics with long polynomial finite-time corrections.

Anomalous Spin Diffusion in One-Dimensional Antiferromagnets

The problem of characterizing low-temperature spin dynamics in antiferromagnetic spin chains has so far remained elusive. Here we reinvestigate it by focusing on isotropic antiferromagnetic chains whose low-energy effective field theory is governed by the quantum nonlinear sigma model. Employing an exact nonperturbative theoretical approach, we analyze the low-temperature behavior in the vicinity of nonmagnetized states and obtain exact expressions for the spin diffusion constant and the NMR relaxation rate, which we compare with previous theoretical results in the literature. Surprisingly, in SU(2)-invariant spin chains in the vicinity of half filling we find a crossover from the semiclassical regime to a strongly interacting quantum regime characterized by zero spin Drude weight and diverging spin conductivity, indicating superdiffusive spin dynamics. The dynamical exponent of spin fluctuations is argued to belong to the Kardar-Parisi-Zhang universality class. Furthermore, by employing numerical time-dependent density matrix renormalization group simulations, we find robust evidence that the anomalous spin transport persists also at high temperatures, irrespective of the spectral gap and integrability of the model.

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.