Quench dynamics of the quantum XXZ chain with staggered interactions: Exact results and simulations on digital quantum computers

TL;DR

This paper provides exact analytical results and quantum computer simulations for quench dynamics in the quantum XXZ chain with staggered interactions, revealing finite-size effects and critical behavior.

Contribution

It derives exact size-independent expressions for entanglement entropies and Loschmidt echoes, and demonstrates quantum simulations on IBM-Q devices for these dynamical quantities.

Findings

Exact size-independent entanglement entropy expressions

Identification of Loschmidt zeros and finite-size scaling

Quantum simulations accurately reproduce analytical results

Abstract

We investigate quench dynamics in the quantum $S=1/2$ XXZ antiferromagnetic chain with staggered and anisotropic interactions in the flat-band limit. Our quench protocol interchanges the odd- and even-bond strengths of a fully dimerized chain, enabling us to derive exact time-dependent states for arbitrary even system sizes by working in the Bell basis. We obtain closed-form, size-independent expressions for the von Neumann and second-order R\'enyi entanglement entropies. We further calculate exact Loschmidt echoes and the corresponding return rate functions across various anisotropies and system sizes, and identify Loschmidt zeros in finite chains. Our analysis reveals distinct finite-size scaling of the Loschmidt echo at critical times with chain length and identifies the precise conditions on the anisotropy parameter governing the periodicity of the dynamical observables. In addition to the analytic study, we perform two types of numerical experiments on IBM-Q quantum devices. First, we use the Hadamard test to estimate the Bell-basis expansion coefficients and reconstruct the dynamical states, achieving accurate entanglement entropies and the Loschmidt echo for small systems. Second, we implement Trotter-error-free time-evolution circuits combined with randomized Pauli measurements. Post-processing via statistical correlations and classical shadows yields reliable estimates of the second-order R\'enyi entanglement entropy and the Loschmidt echo, showing satisfactory agreement with exact results.