Statistical Mechanics of Random Mixed State Ensembles with Fixed Energy

TL;DR

This paper develops a microcanonical ensemble framework for random mixed quantum states with fixed average energy, revealing phase transitions and energy fluctuation properties in spin systems.

Contribution

It introduces a new ensemble for mixed states with fixed energy and links its properties to statistical mechanics concepts.

Findings

Ensemble-averaged density matrix derived under fixed energy constraint.

Exhibition of phase transitions without energetic interactions.

Finite relative energy fluctuations persist in the thermodynamic limit.

Abstract

Mixed state ensembles such as the Bures-Hall and Hilbert-Schmidt measure are probability distributions that characterise the statistical properties of random density matrices and can be used to determine the typical features of mixed quantum states. Here we extend this framework by considering the properties of random states with fixed average energy, and the ensemble-averaged density matrix is derived under this additional physical constraint. This gives rise to a type of microcanonical ensemble for random mixed states and we connect its properties to a statistical mechanical entropy and temperature. Our results are illustrated using a variety of simple spin systems, and we find that they can exhibit exotic features such as phase transitions in the absence of energetic interactions and finite relative energy fluctuations in the thermodynamic limit.