Quantum Monte Carlo calculation of entanglement Renyi entropies for generic quantum systems

TL;DR

This paper introduces a Monte Carlo-based method to calculate the Renyi entropies of subsystems in quantum many-body systems, enabling analysis of entanglement and thermal properties across different temperatures.

Contribution

The authors develop a general scheme for computing Renyi entropies in quantum Monte Carlo simulations, applicable to various models and temperature regimes, including low-temperature entanglement and thermal crossover.

Findings

Quantum spin models in 2D follow an area law for entanglement entropy.

The method efficiently computes entanglement in models with reduced symmetry.

Application to quantum rotor and spin models demonstrates the scheme's versatility.

Abstract

We present a general scheme for the calculation of the Renyi entropy of a subsystem in quantum many-body models that can be efficiently simulated via quantum Monte Carlo. When the simulation is performed at very low temperature, the above approach delivers the entanglement Renyi entropy of the subsystem, and it allows to explore the crossover to the thermal Renyi entropy as the temperature is increased. We implement this scheme explicitly within the Stochastic Series expansion as well as within path-integral Monte Carlo, and apply it to quantum spin and quantum rotor models. In the case of quantum spins, we show that relevant models in two dimensions with reduced symmetry (XX model or hardcore bosons, transverse-field Ising model at the quantum critical point) exhibit an area law for the scaling of the entanglement entropy.