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.
Categories: quant-ph hep-th