Probing Quantum Frustrated Systems via Factorization of the Ground State

TL;DR

This paper investigates the relationship between frustration and ground state factorization in quantum systems, identifying conditions for separability and its implications for understanding complex quantum phases.

Contribution

It determines the exact form of factorized ground states and critical frustration thresholds for various non-solvable spin models, linking frustration to ground state properties.

Findings

Factorized ground states exist below a frustration threshold.

Disentangling transitions mark the limits of mean-field applicability.

Strong frustration prevents classical-like ground state solutions.

Abstract

The existence of definite orders in frustrated quantum systems is related rigorously to the occurrence of fully factorized ground states below a threshold value of the frustration. Ground-state separability thus provides a natural measure of frustration: strongly frustrated systems are those that cannot accommodate for classical-like solutions. The exact form of the factorized ground states and the critical frustration are determined for various classes of nonexactly solvable spin models with different spatial ranges of the interactions. For weak frustration, the existence of disentangling transitions determines the range of applicability of mean-field descriptions in biological and physical problems such as stochastic gene expression and the stability of long-period modulated structures.