Entanglement Spectroscopy using Quantum Monte Carlo

TL;DR

This paper introduces a quantum Monte Carlo-based numerical scheme to reconstruct parts of the entanglement spectrum in quantum many-body systems, enabling insights into quantum phases like the Haldane-Insulator.

Contribution

The paper presents a novel method combining the replica trick and polynomial root solving to reconstruct entanglement spectra from quantum Monte Carlo data.

Findings

Successfully applied to the extended Bose-Hubbard model in 1D

Able to resolve quasi-degeneracy in the entanglement spectrum

Performs best when eigenvalues are not too disparate

Abstract

We present a numerical scheme to reconstruct a subset of the entanglement spectrum of quantum many body systems using quantum Monte Carlo. The approach builds on the replica trick to evaluate particle number resolved traces of the first n of powers of a reduced density matrix. From this information we reconstruct n entanglement spectrum levels using a polynomial root solver. We illustrate the power and limitations of the method by an application to the extended Bose-Hubbard model in one dimension where we are able to resolve the quasi-degeneracy of the entanglement spectrum in the Haldane-Insulator phase. In general the method is able to reconstruct the largest few eigenvalues in each symmetry sector and typically performs better when the eigenvalues are not too different.