Dynamics of entanglement after exceptional quantum quench

TL;DR

This paper studies the dynamics of entanglement after a quantum quench from a critical to an exceptional point in a non-Hermitian SSH model, revealing supersonic modes, multiple light cones, and unique decay and entropy behaviors.

Contribution

It demonstrates the behavior of entanglement and correlation propagation in a non-Hermitian system at an exceptional point, highlighting novel supersonic modes and entropy dynamics.

Findings

Supersonic modes propagate with integer multiples of Fermi velocity.

Fermionic Green's function decays as 1/x^2 at long times.

Entanglement entropy develops plateaus and saturates to a volume law.

Abstract

We investigate a quantum quench from a critical to an exceptional point. The initial state, prepared in the ground state of a critical hermitian system, is time evolved with a non-hermitian SSH model, tuned to its exceptional point. The single particle density matrix exhibits supersonic modes and multiple light cones, characteristic to non-hermitian time evolution. These propagate with integer multiples of the original Fermi velocity. In the long time limit, the fermionic Green's function decays spatially as $1/x^2$, in sharp contrast to the usual $1/x$ decay of non-interacting fermions. The entanglement entropy is understood as if all these supersonic modes arise from independent quasiparticles (though they do not), traveling with the corresponding supersonic light cone velocity. The entropy production rate decreases with time and develops plateaus during the time evolution, signaling the distinct velocities in the propagation of non-local quantum correlations. At late times, the entanglement entropy saturates to a finite value, satisfying a volume law.