Hamiltonian-based dimensional reduction and spectral reconstruction with Wilson-Dirac fermions

Abstract

Motivated by the process of reconstructing real-time spectral functions from Euclidean correlators in lattice QCD, we derive explicit expressions for the fermionic determinant and the propagator of the four-dimensional clover-improved Wilson-Dirac fermions on anisotropic lattices in terms of the three-dimensional Wilson-Dirac Hamiltonian operator. We derive an effective Hamiltonian that governs Euclidean time evolution at finite temporal lattice spacing, and demonstrate its hermiticity and particle-anti-particle symmetry. Our results allow to quantify lattice artifacts of the numerical spectral reconstruction based on Euclidean fermionic correlators at finite temporal lattice spacing.

Contribution to the proceedings of the 42nd International Symposium on Lattice Field Theory (LATTICE2025), Mumbai, India