Understanding the entanglement entropy and spectra of 2D quantum systems through arrays of coupled 1D chains

TL;DR

This paper introduces an algorithm to analyze entanglement properties of 2D quantum systems by modeling them as arrays of coupled 1D chains, confirming area law behavior and identifying critical points through entanglement spectrum analysis.

Contribution

The paper presents a novel algorithm for studying 2D quantum systems' entanglement by mapping them to coupled 1D chains, enabling analysis of entanglement entropy and spectra near criticality.

Findings

Confirmed area law for entanglement entropy in 2D systems.

Identified a logarithmic correction near criticality with an effective central charge.

Demonstrated that entanglement spectrum can detect the critical point.

Abstract

We describe an algorithm for studying the entanglement entropy and spectrum of 2D systems, as a coupled array of $N$ one dimensional chains in their continuum limit. Using the algorithm to study the quantum Ising model in 2D, (both in its disordered phase and near criticality) we confirm the existence of an area law for the entanglement entropy and show that near criticality there is an additive piece scaling as $c_{eff}\log (N)/6$ with $c_{eff} \approx 1$. \textcolor{black}{Studying the entanglement spectrum, we show that entanglement gap scaling can be used to detect the critical point of the 2D model. When short range (area law) entanglement dominates we find (numerically and perturbatively) that this spectrum reflects the energy spectrum of a single quantum Ising chain.