Operator correlations in a quenched non-Hermitian Luttinger liquid

TL;DR

This paper investigates the dynamics of operator correlations in a spinful Luttinger liquid after a non-Hermitian interaction quench, revealing unique features like supersonic modes and dominant superconducting correlations, with distinct differences from Hermitian quenches.

Contribution

It provides exact expressions for operator correlations in a non-Hermitian Luttinger liquid and compares their behavior to Hermitian cases, highlighting new dynamical phenomena.

Findings

Superconducting correlations decay slower than charge and spin-density wave correlations.

Operator correlations merge at long times in non-Hermitian quenches, differing from Hermitian cases.

Luttinger liquid universality persists at long times despite non-Hermitian dynamics.

Abstract

We study operator correlations of a spinful Luttinger liquid after introducing a non-Hermitian interaction quench, yielding supersonic modes and dominant superconducting correlations as signatures of the non-unitary dynamics as well as spin-charge separation. A comparative analysis with the Hermitian counterpart, i.e, when the quench is Hermitian, shows a significant difference in the behavior of the model. We derive exact expressions for different operator correlations and show that the superconducting correlations decay slower than the charge and spin-density wave correlations, especially, within the short-time limit, and at the long-time limit all the operator correlations merge differed only by phase factors in the case of non-hermitian interaction quench whereas they do not merge in the case of Hermitian interaction quench. In both cases known Luttinger liquid universality is retained at the long time limit. We also analyze how the dynamics of operator correlations vary in the presence of anisotropy in the quenching parameters.