Describing the ground state of quantum systems through statistical mechanics

TL;DR

This paper introduces a statistical mechanics framework to analyze the ground state of quantum systems by averaging over non-interacting energy levels, providing new insights into their thermodynamic properties.

Contribution

It proposes a novel thermodynamic interpretation for quantum ground states, applying it to the Hubbard model to explore system-specific entropy behaviors.

Findings

Entropy form varies with the specific quantum system.

Application to Hubbard model reveals system-dependent thermodynamic properties.

Provides a new perspective on quantum ground state analysis.

Abstract

We present a statistical mechanics description to study the ground state of quantum systems. In this approach, averages for the complete system are calculated over the non-interacting energy levels. Taking different interaction parameter, the particles of the system fall into non-interacting microstates, corresponding to different occupation probabilities for these energy levels. Using this novel thermodynamic interpretation we study the Hubbard model for the case of two electrons in two sites and for the half-filled band on a one-dimensional lattice. We show that the form of the entropy depends on the specific system considered.