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

James, Andrew J. A. and Konik, Robert M. (2013). Understanding the entanglement entropy and spectra of 2D quantum systems through arrays of coupled 1D chains. Physical Review B, 87(24), article no. 241103(R).

DOI: https://doi.org/10.1103/PhysRevB.87.241103

Abstract

We describe an algorithm for studying the entanglement entropy and spectrum of two-dimensional (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 ≈ 1. 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.

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