Linear quantum quench in the Heisenberg XXZ chain: time dependent Luttinger model description of a lattice system

TL;DR

This paper investigates the non-equilibrium dynamics of the XXZ Heisenberg chain during linear quenches, comparing numerical and analytical results to validate Luttinger liquid theory in time-dependent lattice systems.

Contribution

It provides a detailed comparison between exact numerical simulations and bosonization analytical results for a quenched lattice system, testing Luttinger liquid theory out of equilibrium.

Findings

Excellent agreement between numerics and analytical predictions.

Validation of Luttinger liquid theory in non-equilibrium conditions.

Quantitative analysis of energy, correlations, and fluctuations during quenches.

Abstract

We study variable-rate linear quenches in the anisotropic Heisenberg (XXZ) chain, starting at the XX point. This is equivalent to switching on a nearest neighbour interaction for hard-core bosons or an interaction quench for free fermions. The physical observables we investigate are: the energy pumped into the system during the quench, the spin-flip correlation function, and the bipartite fluctuations of the z component of the spin in a box. We find excellent agreement between exact numerics (infinite system time-evolving block decimation, iTEBD) and analytical results from bosonization, as a function of the quench time, spatial coordinate and interaction strength. This provides a stringent and much-needed test of Luttinger liquid theory in a non-equilibrium situation.