Abstract
We study the dynamics of a quench-prepared domain wall state released into a system whose unitary time evolution is dictated by the Hamiltonian of the Heisenberg spin-1/2 gapped antiferromagnetic chain. Using exact wavefunctions and their overlaps with the domain wall state allows us to describe the release dynamics to high accuracy, up to the long-time limit, for finite as well as infinite systems. The results for the infinite system allow us to rigorously prove that the system in the gapped regime (Δ>1) cannot thermalize in the strict sense.
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GENERAL SCIENTIFIC SUMMARY Introduction and background. One of the fundamental questions in non-equilibrium physics is: once a quantum system is driven out of equilibrium, will the system relax to a steady state, and, if so, can this state be described by a statistical ensemble? These issues are currently under debate. Most notably, the effects of finite size and integrability might be determinantal, but are not yet well understood.
Main results. We start by preparing a spin system in a domain wall state, and then quench its Hamiltonian to that of the Heisenberg spin-1/2 gapped antiferromagnetic chain. Since the initial state is not an eigenstate of the final Hamiltonian, the unitary time evolution leads to non-equilibrium behaviour. Using exact wavefunctions and their overlaps with the initial state allows us to describe the release dynamics to high accuracy, up to the long-time limit, for finite as well as infinite systems. The results for the infinite system allow us to rigorously prove that the system in the gapped regime (Δ >1) cannot thermalize in the strict sense. Furthermore, we argue that the absence of thermalization can be understood from the properties of the spectrum only, not taking into account the fact that the system is integrable.
Wider implications. The tools developed in this work can be generalized to study a whole class of quenches in a well-controlled manner, and allow for a phenomenological interpretation of the results. The ability to offer a number of results for the finite system as well as in the thermodynamic limit makes a thorough analysis of finite size effects possible.