Lattice fermions with solvable wide range interactions

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 $\ddot{I}€$ leads to a positive classical Hamiltonian ${\mathcal{H}}^R$. The exact solvability of ${\mathcal{H}}^R$ warrants that of a spinless lattice fermion $c_x$, $c_x^{†}$, ${\mathcal{H}}_f^R={\sum }_{x,y\in \mathcal{X}}{c}_x^{†}{\mathcal{H}}^R(x,y)c_y$ 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.

LaTeX2e, 15 pages, no figure