标题： 交错费米子哈密顿量与正方形格点上的离散霍奇-狄拉克算子的等价性 显示英文标题

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

摘要： 我们证明了自由无质量交错费米子（或KS-费米子）哈密顿量等价于$d$维正方形晶格上的离散Hodge-Dirac算子$h\mathbb{Z}^d$。事实上，在其在$\ell^2(2h\mathbb{Z}^d)\otimes\mathbb{C}^{2^d}$上的表示的适当选择下，它们是相同的算子值矩阵。我们采用Nakamura（2024）对交错费米子的表述，以及Miranda-Parra（2023）对正方形晶格上的离散上同调结构的表述。 显示英文摘要

摘要： 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).