A class of solvable models in Condensed Matter Physics

TL;DR

This paper introduces a broad class of fermionic models in condensed matter physics where the equations of motion close, enabling exact analytical solutions for Green's functions across any dimension, with specific one-dimensional examples.

Contribution

It identifies a large class of solvable fermionic models with closed equations of motion, providing exact solutions and a systematic method for determining self-consistent parameters.

Findings

Closed-form Green's functions for the models.

Exact solutions in one-dimensional cases.

Framework applicable to any spatial dimension.

Abstract

In this paper, we show that there is a large class of fermionic systems for which it is possible to find, for any dimension, a finite closed set of eigenoperators and eigenvalues of the Hamiltonian. Then, the hierarchy of the equations of motion closes and analytical expressions for the Green's functions are obtained in terms of a finite number of parameters, to be self-consistently determined. Several examples are given. In particular, for these examples it is shown that in the one-dimensional case it is possible to derive by means of algebraic constraints a set of equations which allow us to determine the self-consistent parameters and to obtain a complete exact solution.