Quantum quench within the gapless phase of the spin-1/2 Heisenberg XXZ spin-chain

TL;DR

This paper investigates the dynamics of spin correlations after a quantum quench in the gapless phase of the spin-1/2 Heisenberg XXZ chain, comparing numerical results with Luttinger liquid predictions.

Contribution

It provides a detailed numerical analysis of post-quench correlation functions and highlights the differing accuracy of Luttinger liquid predictions for transverse and longitudinal correlations.

Findings

Transverse correlations match Luttinger model predictions closely.

Longitudinal correlations show poorer agreement with the Luttinger model.

The difference is attributed to the locality properties of spin operators.

Abstract

We consider an interaction quench in the critical spin-1/2 Heisenberg XXZ chain. We numerically compute the time evolution of the two-point correlation functions of spin operators in the thermodynamic limit and compare the results to predictions obtained in the framework of the Luttinger liquid approximation. We find that the transverse correlation function $\langle S^x_jS^x_{j+\ell}\rangle$ agrees with the Luttinger model prediction to a surprising level of accuracy. The agreement for the longitudinal two-point function $\langle S^z_jS^z_{j+\ell}\rangle$ is found to be much poorer. We speculate that this difference between transverse and longitudinal correlations has its origin in the locality properties of the respective spin operator with respect to the underlying fermionic modes.