Restoration of Ensemble Equivalence by Quantum Fluctuations

TL;DR

This paper investigates how quantum fluctuations introduced by a transverse magnetic field affect the phase diagram and ensemble equivalence in a one-dimensional quantum spin chain with mean-field and nearest-neighbor interactions.

Contribution

It demonstrates that quantum fluctuations can restore ensemble equivalence by eliminating ensemble inequivalence above a critical transverse field.

Findings

Ensemble inequivalence is removed above a threshold transverse field $h_c$.

The phase diagram exhibits only second-order phase transitions for $h > h_c$.

The Hubbard-Stratonovich transformation is effective despite non-commuting operators.

Abstract

We study the thermodynamic phase diagram of a one-dimensional quantum spin chain subjected to both mean-field and nearest-neighbor interactions, and to a transverse magnetic field $h$. The purpose is to determine the effect of the quantum fluctuations, due to the transverse field, on the phase diagram, in particular with respect to the occurrence of ensemble inequivalence. We denote our model as a quantum Nagle-Kardar model. To perform the calculation of the canonical partition function, we show that, due to the presence of the mean-field term, in the thermodynamic limit one can use the Hubbard-Stratonovich transformation in spite of the non-commutativity of the different operators appearing in the Hamiltonian, and we adopt a procedure of successive approximations that lead to the determination of the phase diagram thanks to a scaling property of the phase transition lines. The results show that the ensemble inequivalence, present in the classical Nagle-Kardar model, is removed above a threshold value $h_c$ for the transverse field. For $h$ larger than $h_c$ the phase diagram exhibits only second-order phase transition lines, implying therefore restoration of ensemble equivalence.