Massless fermions in uniform flux background on $T^2\times R$: Vacuum quantum numbers from single-particle filled modes using lattice regulator

TL;DR

This paper investigates the quantum numbers of massless fermions in a uniform flux background on a torus, demonstrating that lattice regularization with overlap fermions accurately reproduces continuum properties and reveals the importance of filled states in the ground state.

Contribution

It provides a lattice analysis of massless fermions in a uniform flux background on $T^2\times R$, showing exact reproduction of continuum zero mode properties and highlighting the role of filled states in ground state quantum numbers.

Findings

Lattice analysis with overlap fermions matches continuum zero mode transformation properties.

Filled single-particle states significantly affect the many-body ground state quantum numbers.

The study extends the understanding of fermions in flux backgrounds from $S^2\times R$ to $T^2\times R$.

Abstract

The quantum numbers of monopoles in $R^3$ in the presence of massless fermions have been analyzed using a uniform flux background in $S^2\times R$ coupled to fermions. An analogous study in $T^2\times R$ is performed by studying the discrete symmetries of the Dirac Hamiltonian in the presence of a static uniform field on $T^2$ with a total flux of $Q$ in the continuum. The degenerate ground states are classified based on their transformation properties under $\frac{\pi}{2}$ rotations of $T^2$ 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.