Quantum Ising chain with boundary dephasing

TL;DR

This paper investigates the effects of boundary dephasing on the quantum Ising chain, revealing a universal N^{-3} scaling of the Liouvillian gap through analytical and numerical methods.

Contribution

It introduces a novel mapping of the boundary dephasing problem to the SSH model with imaginary chemical potential, providing new insights into relaxation dynamics.

Findings

Liouvillian gap scales as N^{-3} with system size

Mapping to SSH model with imaginary chemical potential

Analytical and numerical confirmation of scaling

Abstract

We study the quantum Ising chain with boundary dephasing. By doubling the Hilbert space, the model is mapped to the Su-Schrieffer-Heeger model with imaginary chemical potential at the edges. We show analytically and numerically that the Liouvillian gap, i.e., the inverse relaxation time of the model, scales with the system size $ N $ as $ N^{-3} $.