The bosonic Hubbard model on a three dimensional flat band lattice

TL;DR

This paper studies the bosonic Hubbard model on a 3D flat band lattice, revealing localized eigenstates, exact multi-particle ground states, and a transition from extensive to subextensive entropy at a critical particle number.

Contribution

It constructs exact multi-particle ground states on a 3D flat band lattice and analyzes the entropy scaling at the critical particle number.

Findings

Ground states are constructed by placing particles in localized single-particle states.

At the critical particle number, the ground state entropy scales subextensively as N_c^{2/3}.

Below the critical density, the entropy is extensive.

Abstract

The lowest eigenstates of the hopping matrix on the line graph of a cubic lattice with periodic boundary conditions are highly degenerate, they form a lowest flat band. Further, these states are localized. If one considers a repulsive bosonic Hubbard model on this lattice it is possible to construct exact multi-particle ground states simply by putting particles in the localized single particle ground states such that they avoid each other. This can be done up to a certain critical particle number $N_c$. We prove that at this particle number the ground state entropy is subextensive $\propto N_c^{2/3}$. For lower densities the entropy is extensive. We further show that the problem is related to the number of 4-cycle decompositions of the cubic lattice with periodic boundary conditions.