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.
@article{arxiv.1305.6536,
title = {Entanglement Spectroscopy using Quantum Monte Carlo},
author = {Chia-Min Chung and Lars Bonnes and Pochung Chen and Andreas M. Läuchli},
journal= {arXiv preprint arXiv:1305.6536},
year = {2014}
}