Lattice fermions with solvable wide range interactions

TL;DR

This paper constructs exactly solvable lattice fermion models with wide-range interactions using reversible Markov chains derived from orthogonal polynomials, providing explicit examples and a new solvability framework.

Contribution

It introduces a novel method to build exactly solvable lattice fermion models based on reversible Markov chains linked to orthogonal polynomials, expanding solvable models in quantum many-body physics.

Findings

Explicit construction of lattice fermion models with wide-range interactions.

Demonstration of solvability based on Markov chain reversibility.

Presentation of several concrete examples of such fermion systems.

Abstract

Exactly solvable (spinless) lattice fermions with wide range interactions are constructed explicitly based on {\em exactly solvable stationary and reversible Markov chains} $\mathcal{K}^R$ reported a few years earlier by Odake and myself. The reversibility of $\mathcal{K}^R$ with the stationary distribution $\pi$ leads to a positive classical Hamiltonian $\mathcal{H}^R$. The exact solvability of $\mathcal{H}^R$ warrants that of a spinless lattice fermion $c_x$, $c_x^\dagger$, $\mathcal{H}^R_f=\sum_{x,y\in\mathcal{X}}c_x^\dagger\mathcal{H}^R(x,y) c_y$ based on the principle advocated recently by myself. The reversible Markov chains $\mathcal{K}^R$ are constructed by convolutions of the orthogonality measures of the discrete orthogonal polynomials of Askey scheme. Several explicit examples of the fermion systems with wide range interactions are presented.