Ground-state factorization and correlations with broken symmetry

¹ MATIS-INFM-CNR & Dipartimento di Fisica e Astronomia - 95123 Catania, Italy, EU
² NEST, Scuola Normale Superiore & Istituto Nanoscienze-CNR - Piazza dei Cavalieri 7, I-56126 Pisa, Italy, EU
³ Perimeter Institute for Theoretical Physics - 31 Caroline St. N, Waterloo ON, N2L 2Y5, Canada

^a lamico@dmfci.unict.it

Received: 28 July 2011
Accepted: 29 August 2011

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.