Canonical Thermal Pure Quantum State

TL;DR

This paper introduces the canonical thermal pure quantum (TPQ) state, a single pure state representation of a quantum system's thermal equilibrium, unifying different ensembles and simplifying practical calculations in statistical mechanics.

Contribution

The paper constructs the canonical TPQ state, demonstrating its equivalence to traditional ensembles and highlighting its advantages for practical applications in quantum statistical mechanics.

Findings

Canonical TPQ states reproduce thermodynamic variables.

Different ensemble TPQ states are related by simple transformations.

TPQ formulation simplifies practical calculations in quantum systems.

Abstract

A thermal equilibrium state of a quantum many-body system can be represented by a typical pure state, which we call a thermal pure quantum (TPQ) state. We construct the canonical TPQ state, which corresponds to the canonical ensemble of the conventional statistical mechanics. Only a single realization of the TPQ state gives all variables of statistical-mechanical interest. We show that TPQ states corresponding to different ensembles give identical thermodynamic results, and they are related by simple analytic transformations. We have thus completed the TPQ formulation of statistical mechanics. We also show that it has great advantages in practical applications.