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

2024/02/11 by Nakamura, Shu
#81Q35 #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2402.07094

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 hℤ^d. In fact, they are identical operator valued matrices under suitable choices of their representations on ℓ²(2hℤ^d)⊗ℂ^2d. We employ the formulations of the staggered fermion by Nakamura (2024), and the discrete cohomology structure on the square lattices by Miranda-Parra (2023).

Related

• Remarks on discrete Dirac operators and their continuum limits
• A path-integral representation of the free one-flavour staggered-fermion determinant
• A Lattice Fermion Doublet With A Generalization Of The Ginsparg-Wilson Relation
• Geometric Origin of Staggered Fermion: Direct Product K-Cycle
• Symmetries and Anomalies of Hamiltonian Staggered Fermions