Quantum quenches in the anisotropic spin-1/2 Heisenberg chain: different approaches to many-body dynamics far from equilibrium

TL;DR

This paper investigates the non-equilibrium dynamics of the antiferromagnetic order in the anisotropic Heisenberg chain after a sudden quench, using numerical, analytical, and exact methods to understand decay behaviors and the applicability of low-energy theories.

Contribution

It provides a comprehensive comparison of numerical and analytical approaches to quantum quenches in the Heisenberg chain, highlighting which phenomena are captured by low-energy theories and which are inherently quantum.

Findings

Order parameter decays exponentially in most cases

Oscillatory and non-oscillatory dynamics observed

Analytical methods reveal the role of high-energy spectrum

Abstract

Recent experimental achievements in controlling ultracold gases in optical lattices open a new perspective on quantum many-body physics. In these experimental setups it is possible to study coherent time evolution of isolated quantum systems. These dynamics reveal new physics beyond the low-energy properties usually relevant in solid-state many-body systems. In this paper we study the time evolution of antiferromagnetic order in the Heisenberg chain after a sudden change of the anisotropy parameter, using various numerical and analytical methods. As a generic result we find that the order parameter, which can show oscillatory or non-oscillatory dynamics, decays exponentially except for the effectively non-interacting case of the XX limit. For weakly ordered initial states we also find evidence for an algebraic correction to the exponential law. The study is based on numerical simulations using a numerical matrix product method for infinite system sizes (iMPS), for which we provide a detailed description and an error analysis. Additionally, we investigate in detail the exactly solvable XX limit. These results are compared to approximative analytical approaches including an effective description by the XZ-model as well as by mean-field, Luttinger-liquid and sine-Gordon theories. This reveals which aspects of non-equilibrium dynamics can as in equilibrium be described by low-energy theories and which are the novel phenomena specific to quantum quench dynamics. The relevance of the energetically high part of the spectrum is illustrated by means of a full numerical diagonalization of the Hamiltonian.