Topological classification of dynamical quantum phase transitions in the xy chain

Abstract

Understanding the properties of far-from-equilibrium quantum systems is becoming a major challenge of both fundamental and applied physics. For instance, the lack of thermalization in integrable and (many body) localized systems provides new insights in the understanding of the relaxation dynamics of quantum phases. On a more applicative side, the possibility of exploiting the properties of far-from-equilibrium states, for example in pump-probe experiments, opens unprecedented scenarios. The effort in providing a classification of far-from-equilibrium phases, in terms of local or topological order parameters, is hence intense. In this context, the concept of Dynamical Quantum Phase Transition (DQPT) has been introduced. A DQPT is (roughly) defined as a zero of the Loschmidt-Echo as a function of time and represents a natural non-equilibrium counterpart of a thermal phase transition. Here, we investigate the DQPTs occurring in the quantum xy chain subject to a quantum quench of finite duration. We show that the number of distinct DQPTs can vary as the duration of the quantum quench is varied. However, the parity of such number only depends on the pre-quench and post-quench Hamiltonians and is related to a topological invariant.

The Loschmidt Index

“…There are at least two other notions of topological invariants for DQPTs in the literature [35][36][37]. The topological invariant described by Budich and Heyl [37] is time-dependent.…”

“…Unlike the number of nodes, these Chern numbers are only nontrivial when the DQPT is topologically protected [35]. The topological invariant of Yang, Li and Chen was recently generalized in [36] to quantum quenches of finite duration.…”

A Short Review of One-Dimensional Wigner Crystallization

“…where ψ j are spinless fermions. At the end of this procedure one obtains a bosonized low energy Hamiltonian H σ given by [90,91]…”

Signature of Generalized Gibbs Ensemble Deviation from Equilibrium: Negative Absorption Induced by a Local Quench

“…In particular, in the case of integrable quantum systems [32], the post-quench dynamics is restricted by a complete set {Î α } of local constants of motions commuting with the post-quench Hamiltonian [33]. This implies that, if an out of equilibrium steady state is reached, it can be described by a Generalized Gibbs Ensemble (GGE) density matrix [7,[34][35][36][37][38][39][40][41]…”

“…where the Lagrange multipliers {λ α } are determined by the pre-quench state and uniquely characterize the GGE. On the theoretical side, there is a growing consensus that the GGE hypothesis works both for homogeneous [7,[34][35][36][37][38][39][40][41] and inhomogeneous [17,18,[42][43][44] quenches. However, only a few experimental GGE signatures have been observed so far, mostly limited to trapped one-dimensional Bose gases [45].…”