Massless fermions in uniform flux background on T2×R : Vacuum quantum numbers from single-particle filled modes using lattice regulator

Abstract

The quantum numbers of monopoles in R3 in the presence of massless fermions have been analyzed using a uniform flux background in S2×R coupled to fermions. An analogous study in T2×R is performed by studying the discrete symmetries of the Dirac Hamiltonian in the presence of a static uniform field on T2 with a total flux of Q in the continuum. The degenerate ground states are classified based on their transformation properties under π2 rotations of T2 that leave the background field invariant. We find that the lattice analysis with overlap fermions exactly reproduces the transformation properties of the single-particle zero modes in the continuum. Whereas the transformation properties of the single-particle negative energy states can be studied in the continuum and the lattice, we are also able to study the transformation properties and the particle number (charge) of the many-body ground state on a finite lattice, and we show that the contributions from the fully filled single-particle states cannot be ignored. Published by the American Physical Society 2025