Exact solution of the 1D Hubbard model in the atomic limit with inter-site magnetic coupling

TL;DR

This paper provides the first exact solution of the 1D extended Hubbard model with magnetic interactions in the atomic limit, revealing complex phase behavior and excitations at zero and finite temperatures.

Contribution

It introduces an exact solution for the 1D extended Hubbard model with spin-spin interactions using Green's functions and the Composite Operator Method.

Findings

Rich phase diagram with magnetic orders at zero temperature

Coexistence of charge and spin orderings at commensurate filling

Presence of low-temperature charge and spin excitations near phase boundaries

Abstract

In this paper we present for the first time the exact solution in the narrow-band limit of the 1D extended Hubbard model with nearest-neighbour spin-spin interactions described by an exchange constant J. An external magnetic field h is also taken into account. This result has been obtained in the framework of the Green's functions formalism, using the Composite Operator Method. By means of this theoretical background, we have studied some relevant features such as double occupancy, magnetization, spin-spin and charge-charge correlation functions and derived a phase diagram for both ferro (J>0) and anti-ferro (J<0) coupling in the limit of zero temperature. We also report a study on density of states, specific heat, charge and spin susceptibilities. In the limit of zero temperature, we show that the model exhibits a very rich phase diagram characterized by different magnetic orders and by the coexistence of charge and spin orderings at commensurate filling. Moreover, our analysis at finite temperature of density of states and response functions shows the presence of low-temperature charge and spin excitations near the phase boundaries.