Entanglement entropy with localized and extended interface defects

TL;DR

This paper investigates how localized and extended interface defects affect entanglement entropy scaling in a critical quantum Ising chain, revealing different behaviors in equilibrium and non-equilibrium states.

Contribution

It provides a detailed analysis of entanglement entropy scaling with interface defects, highlighting the continuous variation of effective central charge for localized defects and saturation for extended defects.

Findings

Localized defects lead to a logarithmic increase in entropy with system size and time.

Extended defects cause entropy saturation in equilibrium but logarithmic growth out of equilibrium.

The effective central charge varies continuously with defect strength for localized defects.

Abstract

The quantum Ising chain of length, L, which is separated into two parts by localized or extended defects is considered at the critical point where scaling of the interface magnetization is non-universal. We measure the entanglement entropy between the two halves of the system in equilibrium, as well as after a quench, when the interaction at the interface is changed for time t>0. For the localized defect the increase of the entropy with log(L) or with log(t) involves the same effective central charge, which is a continuous function of the strength of the defect. On the contrary for the extended defect the equilibrium entropy is saturated, but the non-equilibrium entropy has a logarithmic time-dependence the prefactor of which depends on the strength of the defect.