# Measuring von Neumann entanglement entropies without wave functions

## TL;DR

This paper introduces a novel method to measure von Neumann entanglement entropy in quantum many-body systems without needing the wave function, using thermodynamic properties of entanglement Hamiltonians applicable to simulations and experiments.

## Contribution

The authors develop a thermodynamic approach to determine entanglement entropy directly, bypassing the need for wave function access, and validate it on various quantum systems.

## Key findings

- Successfully measured entanglement entropy in quantum spin chains and 2D magnets.
- Identified the onset of area law behavior and number of Goldstone bosons.
- Confirmed a conjecture on geometric entanglement at critical points.

## Abstract

We present a method to measure the von Neumann entanglement entropy of ground states of quantum many-body systems which does not require access to the system wave function. The technique is based on a direct thermodynamic study of entanglement Hamiltonians, whose functional form is available from field theoretical insights. The method is applicable to classical simulations such as quantum Monte Carlo methods, and to experiments that allow for thermodynamic measurements such as the density of states, accessible via quantum quenches. We benchmark our technique on critical quantum spin chains, and apply it to several two-dimensional quantum magnets, where we are able to unambiguously determine the onset of area law in the entanglement entropy, the number of Goldstone bosons, and to check a recent conjecture on geometric entanglement contribution at critical points described by strongly coupled field theories.