Degeneracy of Many-body Quantum States in an Optical Lattice with a Uniform Magnetic Field

TL;DR

This paper proves a theorem linking the degeneracy of many-body quantum states in a lattice under a magnetic field to particle number and flux ratio, revealing complex ground state structures.

Contribution

It introduces a theorem connecting state degeneracy with system parameters and analyzes the nature of the quantum ground state in such systems.

Findings

Degeneracy depends on particle number and flux ratio.

Ground state is fragmented, not mean-field, even with weak interactions.

Quantum interference effects influence tunneling paths.

Abstract

We prove a theorem that shows the degeneracy of many-body states depends on total particle number and flux filling ratio, for particles in a periodic lattice and under a uniform magnetic field. Non-interacting fermions and weakly interacting bosons are given as two examples. For the later case, this phenomena can also be understood in terms of destructive quantum interferences of multiple symmetry related tunneling paths between classical energy minima, which is reminiscent of the spin-parity effect discovered in magnetic molecular cluster. We also show that the quantum ground state of a mesoscopic number of bosons in this system is not a simple mean-field state but a fragmented state even for very weak interactions.