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arXiv · 2410.08467

Lattice fermions with solvable wide range interactions

Ryu Sasaki
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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.

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Ryu Sasaki. 2024-10-11. Lattice fermions with solvable wide range interactions. https://arxiv.org/abs/2410.08467

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