Stable Quantum Monte Carlo Simulations for Entanglement Spectra of Interacting Fermions

TL;DR

This paper develops a numerically stable quantum Monte Carlo method to compute entanglement spectra in interacting fermion systems, demonstrated on the Kane-Mele Hubbard model, with potential applications to bosonic systems.

Contribution

It unifies two existing methods for entanglement entropy calculation, enabling stable computation of entanglement spectra at strong coupling.

Findings

Successfully computed entanglement spectra across a quantum phase transition.

Demonstrated equivalence of two Monte Carlo approaches for entanglement measures.

Method applicable to both fermionic and bosonic systems.

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.