Exact solution of the 1D Hubbard model with NN and NNN interactions in the narrow-band limit

TL;DR

This paper provides an exact analytical solution for the phase diagram of the 1D Hubbard model with NN and NNN interactions in the atomic limit, using an extended transfer matrix method.

Contribution

It introduces an extended transfer matrix approach to exactly solve the 1D Hubbard model with extended interactions in the zero-temperature limit.

Findings

Comprehensive T=0 phase diagram with multiple phases

Analytic expressions for ground state energies

Method applicable to other extended 1D models

Abstract

We present the exact solution, obtained by means of the Transfer Matrix (TM) method, of the 1D Hubbard model with nearest-neighbor (NN) and next-nearest-neighbor (NNN) Coulomb interactions in the atomic limit (t=0). The competition among the interactions ($U$, $V_1$, and $V_2$) generates a plethora of T=0 phases in the whole range of fillings. $U$, $V_1$, and $V_2$ are the intensities of the local, NN and NNN interactions, respectively. We report the T=0 phase diagram, in which the phases are classified according to the behavior of the principal correlation functions, and reconstruct a representative electronic configuration for each phase. In order to do that, we make an analytic limit $T\to 0$ in the transfer matrix, which allows us to obtain analytic expressions for the ground state energies even for extended transfer matrices. Such an extension of the standard TM technique can be easily applied to a wide class of 1D models with the interaction range beyond NN distance, allowing for a complete determination of the T=0 phase diagrams.