The half-filled Hubbard chain in the Composite Operator Method: A comparison with Bethe Ansatz

TL;DR

This paper applies the Composite Operator Method to the half-filled 1D Hubbard model, achieving results consistent with Bethe Ansatz and demonstrating its potential for calculating properties beyond Bethe Ansatz capabilities.

Contribution

It introduces the use of the Composite Operator Method with a static approximation for the half-filled Hubbard chain, providing accurate ground-state properties and showing its applicability for further property evaluations.

Findings

Ground-state energy matches Bethe Ansatz results

Double occupancy and specific heat agree with Bethe Ansatz

Method can evaluate properties like correlation functions beyond Bethe Ansatz

Abstract

The one-dimensional Hubbard model at half-filling is studied in the framework of the Composite Operator Method using a static approximation. A solution characterized by strong antiferromagnetic correlations and a gap for any nonzero on-site interaction U is found. The corresponding ground-state energy, double occupancy and specific heat are in excellent agreement with those obtained within the Bethe Ansatz. These results show that the Composite Operator Method is an appropriate framework for the half-filled Hubbard chain and can be applied to evaluate properties, like the correlation functions, which cannot be obtained by means of the Bethe Ansatz, except for some limiting cases.