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arXiv · 2402.07094

Equivalence of the staggered fermion Hamiltonan and the discrete Hodge-Dirac operator on square lattices

Shu Nakamura
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Abstract

We show that the free massless staggered fermion (or the KS-fermion) Hamiltonian is equivalent to a discrete Hodge-Dirac operator on the $d$-dimensional square lattice $h\mathbb{Z}^d$. In fact, they are identical operator valued matrices under suitable choices of their representations on $\ell^2(2h\mathbb{Z}^d)\otimes\mathbb{C}^{2^d}$. We employ the formulations of the staggered fermion by Nakamura (2024), and the discrete cohomology structure on the square lattices by Miranda-Parra (2023).

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Shu Nakamura. 2024-02-11. Equivalence of the staggered fermion Hamiltonan and the discrete Hodge-Dirac operator on square lattices. https://arxiv.org/abs/2402.07094

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