# Quantum quench in PT-symmetric Luttinger liquid

## TL;DR

This paper investigates the non-equilibrium dynamics of a PT-symmetric Luttinger liquid after a quantum quench, revealing faster-than-light-cone correlations and extending LL universality to non-hermitian systems.

## Contribution

It introduces the analysis of non-hermitian LL dynamics post-quench, highlighting supersonic modes and extending LL universality to non-hermitian regimes.

## Key findings

- Correlations propagate faster than Lieb-Robinson bound.
- Supersonic modes travel with velocities multiple of the light-cone velocity.
- Quantum information disperses faster in non-hermitian systems.

## Abstract

A Luttinger liquid (LL) describes low energy excitations of many interacting one dimensional systems, and exhibits universal response both in and out of equilibrium. We analyze its behaviour in the non-hermitian realm after quantum quenching to a PT-symmetric LL by focusing on the fermionic single particle density matrix. For short times, we demonstrate the emergence of unique phenomena, characteristic to non-hermitian systems, that correlations propagate faster than the conventional maximal speed, known as the Lieb-Robinson bound. These emergent supersonic modes travel with velocities that are multiples of the conventional light-cone velocity. This behaviour is argued to be generic for correlators in non-hermitian systems. In the long time limit, we find typical LL behaviour, extending the LL universality to the non-equilibrium non-hermitian case. Our analytical results are benchmarked numerically and indicate that the dispersal of quantum information is much faster in non-hermitian systems.