Universal shape-dependence of quantum entanglement in disordered magnets

TL;DR

This paper investigates how quantum entanglement in disordered two-dimensional quantum magnets depends on subsystem shape, revealing universal corner contributions and shape-dependent differences across phase transition universality classes.

Contribution

It demonstrates the shape dependence of corner entanglement contributions in disordered quantum systems, extending understanding beyond conformally invariant models.

Findings

Corner entanglement contribution is universal across fixed points.

Shape dependence of entanglement varies with universality class.

Subsystem shape can reveal universal information about phase transitions.

Abstract

Disordered quantum magnets are not only experimentally relevant, but offer efficient computational methodologies to calculate the low energy states as well as various measures of quantum correlations. Here, we present a systematic analysis of quantum entanglement in the paradigmatic random transverse-field Ising model in two dimensions, using an efficient implementation of the asymptotically exact strong disorder renormalization group method. The phase diagram is known to be governed by three distinct infinitely disordered fixed points (IDFPs) that we study here. For square subsystems, it has been recently established that quantum entanglement has a universal logarithmic correction due to the corners of the subsystem at all three IDFPs. This corner contribution has been proposed as an "entanglement susceptibility", a useful tool to locate the phase transition and to measure the correlation length critical exponent. Towards a deeper understanding, we quantify how the corner contribution depends on the shape of the subsystem. While the corner contribution remains universal, the shape-dependence is qualitatively different in each universality class, also confirmed by line segment subsystems, a special case of skeletal entanglement. Therefore, unlike in conformally invariant systems, in general different subsystem shapes are versatile probes to unveil new universal information on the phase transitions in disordered quantum systems.