Reading entanglement in terms of spin configurations in quantum magnets

TL;DR

This paper introduces a formalism to interpret quantum entanglement in magnetic systems by analyzing spin configurations, applying it to the Heisenberg model, and using Quantum Monte Carlo simulations to explore entanglement behavior under magnetic fields.

Contribution

It develops a novel method to connect magnetic observables with quantum entanglement properties in many-body spin systems.

Findings

Entanglement can be characterized through probability distributions of spin states.

Application to the Heisenberg model reveals how entanglement varies with magnetic field.

Quantum Monte Carlo simulations effectively capture entanglement dynamics.

Abstract

We consider a quantum many-body system made of $N$ interacting $S{=}1/2$ spins on a lattice, and develop a formalism which allows to extract, out of conventional magnetic observables, the quantum probabilities for any selected spin pair to be in maximally entangled or factorized two-spin states. This result is used in order to capture the meaning of entanglement properties in terms of magnetic behavior. In particular, we consider the concurrence between two spins and show how its expression extracts information on the presence of bipartite entanglement out of the probability distributions relative to specific sets of two-spin quantum states. We apply the above findings to the antiferromagnetic Heisenberg model in a uniform magnetic field, both on a chain and on a two-leg ladder. Using Quantum Monte Carlo simulations, we obtain the above probability distributions and the associated entanglement, discussing their evolution under application of the field.