Ground state factorization and correlations with broken symmetry

TL;DR

This paper investigates the collective nature of ground state factorization in quantum many-body systems, analyzing quantum discord in the XY model, revealing exponential scaling laws and universal thermal crossover behaviors.

Contribution

It demonstrates that ground state factorization is governed by exponential scaling of quantum discord and explores thermal effects near quantum phase transitions.

Findings

Quantum discord exhibits exponential scaling at the factorizing field.

Thermal effects show universal scaling near quantum critical points.

Factorization leads to unique low-temperature correlation patterns.

Abstract

We show how the phenomenon of factorization in a quantum many body system is of collective nature. To this aim we study the quantum discord $Q$ in the one dimensional XY model in a transverse field. We analyze the behavior of $Q$ at both the critical point and at the non critical factorizing field. The factorization is found to be governed by an exponential scaling law for $Q$. We also address the thermal effects fanning out from the anomalies occurring at zero temperature. Close to the quantum phase transition, $Q$ exhibits a finite-temperature crossover with universal scaling behavior, while the factorization phenomenon results in a non trivial pattern of correlations present at low temperature.