Stable Quantum Monte Carlo Simulations for Entanglement Spectra of Interacting Fermions

Abstract

We show that the two recently proposed methods to compute Renyi entanglement entropies in the realm of determinant quantum Monte Carlo methods for fermions are in principle equivalent, but differ in sampling strategies. The analogy allows to formulate a numerically stable calculation of the entanglement spectrum at strong coupling. We demonstrate the approach by studying static and dynamical properties of the entanglement hamiltonian across the interaction driven quantum phase transition between a topological insulator and quantum antiferromagnet in the Kane-Mele Hubbard model. The formulation is not limited to fermion systems and can readily be adapted to world-line based simulations of bosonic systems.

8 pages, 5 figures

References in corpus (5)

• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Correlation effects in two-dimensional topological insulators
• Renyi Entanglement Entropy of Interacting Fermions Calculated Using Continuous-Time Quantum Monte Carlo Method
• Renyi Entropies of Interacting Fermions from Determinantal Quantum Monte Carlo Simulations
• Topological Invariant and Quantum Spin Models from Magnetic π Fluxes in Correlated Topological Insulators

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