Lattice fermions with solvable wide range interactions
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929537768488960 |
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| author | Sasaki, Ryu |
| author_facet | Sasaki, Ryu |
| contents | 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 $π$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_08467 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Lattice fermions with solvable wide range interactions Sasaki, Ryu Quantum Physics High Energy Physics - Theory 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 $π$ 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. |
| title | Lattice fermions with solvable wide range interactions |
| topic | Quantum Physics High Energy Physics - Theory |
| url | https://arxiv.org/abs/2410.08467 |