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arXiv:1404.4062 · Physical Review Letters

“Light-Cone” Dynamics After Quantum Quenches in Spin Chains

Lars Bonnes, Fabian H. L. Eßler, Andreas Martin Läuchli

Published Oct 30, 2014• 244 citations
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Abstract

Signal propagation in the nonequilibrium evolution after quantum quenches has recently attracted much experimental and theoretical interest. A key question arising in this context is what principles, and which of the properties of the quench, determine the characteristic propagation velocity. Here we investigate such issues for a class of quench protocols in one of the central paradigms of interacting many-particle quantum systems, the spin-1/2 Heisenberg XXZ chain. We consider quenches from a variety of initial thermal density matrices to the same final Hamiltonian using matrix product state methods. The spreading velocities are observed to vary substantially with the initial density matrix. However, we achieve a striking data collapse when the spreading velocity is considered to be a function of the excess energy. Using the fact that the XXZ chain is integrable, we present an explanation of the observed velocities in terms of "excitations" in an appropriately defined generalized Gibbs ensemble.

DOI
10.1103/physrevlett.113.187203

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Signal propagation in the nonequilibrium evolution after quantum quenches has recently attracted much experimental and theoretical interest. A key question arising in this context is what principles, and which of the properties of the quench, determine the characteristic propagation velocity. Here we investigate such issues for a class of quench protocols in one of the central paradigms of interacting many-particle quantum systems, the spin-1/2 Heisenberg XXZ chain. We consider quenches from a variety of initial thermal density matrices to the same final Hamiltonian using matrix product state methods. The spreading velocities are observed to vary substantially with the initial density matrix. However, we achieve a striking data collapse when the spreading velocity is considered to be a function of the excess energy. Using the fact that the XXZ chain is integrable, we present an explanation of the observed velocities in terms of "excitations" in an appropriately defined generalized Gibbs ensemble.
We investigate the out-of-equilibrium dynamics after a local quench that connects two spin-1/2 XXZ chains prepared in the ground state of the Hamiltonian in different phases, one in the ferromagnetic phase and the other in the critical phase. We analyze the time evolution of the on-site magnetization and bipartite entanglement entropy via adaptive time-dependent density matrix renormalization group. In systems with short-range interactions, such as the one we consider, the velocity of information transfer is expected to be bounded, giving rise to a light-cone effect. Interestingly, our results show that, when the anisotropy parameter of the critical chain is sufficiently close to that of the isotropic ferromagnet, the light cone is determined by the velocity of spin-wave bound states that propagate faster than single-particle (``spinon'') excitations. Furthermore, we investigate how the system approaches equilibrium in the inhomogeneous ground state of the connected system, in which the ferromagnetic chain induces a nonzero magnetization in the critical chain in the vicinity of the interface.
The time evolution and stationary behaviour of local observables is studied after a quantum quench of the magnetic field in the transverse field Ising chain, when the initial state is chosen as an excited state of the pre-quench Hamiltonian. Relaxation to the Generalized Gibbs Ensemble is proved. Equal-time longitudinal two point function and entanglement entropy are analytically derived for a class of excited states which confirm the light-cone spreading of correlations also starting from excited states.
The past few years have witnessed the development of a comprehensive theory to describe integrable systems out of equilibrium, in which the Bethe ansatz formalism has been tailored to address specific problems arising in this context. While most of the work initially focused on the study of prototypical models such as the well-known Heisenberg chain, many theoretical results have been recently extended to a class of more complicated nested\it{nested}nested integrable systems, displaying different species of quasiparticles. Still, in the simplest context of quantum quenches, the vast majority of theoretical predictions have been numerically verified only in systems with an elementary Bethe ansatz description. In this work, we fill this gap and present a direct numerical test of some results presented in the recent literature for nested systems, focusing in particular on the Lai-Sutherland model. Using time-dependent density matrix renormalization group and exact diagonalization methods, we compute the spreading of both correlation functions and entanglement entropy after a quench from a simple class of product initial states. This allows us to test the validity of the nested version of a conjectured formula, based on the quasiparticle picture, for the growth of the entanglement entropy, and the Bethe ansatz predictions for the "light-cone" velocity of correlation functions.
We study the nonequilibrium time evolution of the spin-1/2 anisotropic Heisenberg (XXZ) spin chain, with a choice of dimer product and Néel states as initial states. We investigate numerically various short-ranged spin correlators in the long-time limit and find that they deviate significantly from predictions based on the generalized Gibbs ensemble (GGE) hypotheses. By computing the asymptotic spin correlators within the recently proposed quench-action formalism [Phys. Rev. Lett. 110, 257203 (2013)], however, we find excellent agreement with the numerical data. We, therefore, conclude that the GGE cannot give a complete description even of local observables, while the quench-action formalism correctly captures the steady state in this case.
Abstract The past few years have witnessed the development of a comprehensive theory to describe integrable systems out of equilibrium, in which the Bethe ansatz formalism has been tailored to address specific problems arising in this context. While most of the work initially focused on the study of prototypical models such as the well-known Heisenberg chain, many theoretical results have been recently extended to a class of more complicated nested integrable systems, displaying different species of quasiparticles. Still, in the simplest context of quantum quenches, the vast majority of theoretical predictions have been numerically verified only in systems with an elementary Bethe ansatz description. In this work, we fill this gap and present a direct numerical test of some results presented in the recent literature for nested systems, focusing in particular on the Lai–Sutherland model. Using time-dependent density matrix renormalization group and exact diagonalization methods, we compute the spreading of both correlation functions and entanglement entropy after a quench from a simple class of product initial states. This allows us to test the validity of the nested version of a conjectured formula, based on the quasiparticle picture, for the growth of the entanglement entropy, and the Bethe ansatz predictions for the ‘light-cone’ velocity of correlation functions.