Entanglement Spectra of Interacting Fermions in Quantum Monte Carlo Simulations

Abstract

In a recent article T. Grover [Phys. Rev. Lett. 111, 130402 (2013)] introduced a simple method to compute Renyi entanglement entropies in the realm of the auxiliary field quantum Monte Carlo algorithm. Here, we further develop this approach and provide a stabilization scheme to compute higher order Renyi entropies and an extension to access the entanglement spectrum. The method is tested on systems of correlated topological insulators.

7+ pages, 5 figures

References in corpus (6)

• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Identifying Topological Order by Entanglement Entropy
• Some formal results for the valence bond basis
• Valence Bond Entanglement Entropy
• Momentum-dependent pseudogaps in the half-filled two-dimensional Hubbard model
• Topological Invariant and Quantum Spin Models from Magnetic π Fluxes in Correlated Topological Insulators

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