Quantum Entanglement of Interacting Fermions in Monte Carlo

TL;DR

This paper introduces a novel method to compute entanglement properties of interacting fermionic systems using Monte Carlo techniques by expressing their reduced density matrices as sums of free fermion operators.

Contribution

The authors develop a decomposition of interacting fermion entanglement structures enabling Renyi entropy calculations via Determinantal Quantum Monte Carlo.

Findings

Entanglement entropy can be computed for interacting fermions.

Method applies to ground state and thermal states.

Efficient for systems simulated with DQMC.

Abstract

Given a specific interacting quantum Hamiltonian in a general spatial dimension, can one access its entanglement properties, such as, the entanglement entropy corresponding to the ground state wavefunction? Even though progress has been made in addressing this question for interacting bosons and quantum spins, as yet there exist no corresponding methods for interacting fermions. Here we show that the entanglement structure of interacting fermionic Hamiltonians has a particularly simple form -- the interacting reduced density matrix can be written as a sum of operators that describe free fermions. This decomposition allows one to calculate the Renyi entropies for Hamiltonians which can be simulated via Determinantal Quantum Monte Carlo, while employing the efficient techniques hitherto available only for free fermion systems. The method presented works for the ground state, as well as for the thermally averaged reduced density matrix.