Grand Canonical Partition Function of a 2-dimensional Hubbard Model

TL;DR

This paper introduces a Monte Carlo-based method to analyze the phase structure of the 2D Hubbard model, revealing phase transitions and pairing tendencies at low temperatures through the grand canonical partition function.

Contribution

It presents a novel numerical approach to study the 2D Hubbard model's phase transitions and pairing phenomena using the grand canonical partition function and Yang-Lee zeros.

Findings

Evidence of a phase transition at zero temperature and below half-filling.

Calculation of hole pairing energy at low temperatures.

Analysis of the dependence of hole occupation on chemical potential.

Abstract

We present a new technique for a numerical analysis of the phase structure of the 2D Hubbard model as a function of the hole chemical potential. The grand canonical partition function for the model is obtained via Monte Carlo simulations. The dependence of the hole occupation number on the chemical potential and the temperature is evaluated. These calculations, together with a study of the Yang-Lee zeros of the grand canonical partition function, show evidence of a phase transition at zero temperature and particle density below half-filling. The binding energy of a pair of holes is calculated in the low temperature regime and the possibility for pairing is explored.