Properties of Hubbard models with degenerate localized single particle eigenstates

TL;DR

This paper investigates the properties of Hubbard models on special lattices with highly degenerate localized single-particle states, constructing multi-particle ground states and analyzing residual entropy at zero temperature.

Contribution

It introduces a method to construct such lattices in arbitrary dimensions and characterizes the ground states and residual entropy of the models.

Findings

Constructed lattices with localized eigenstates in arbitrary dimensions.

Explicitly constructed multi-particle ground states for certain electron numbers.

Identified finite residual entropy at zero temperature.

Abstract

We consider the repulsive Hubbard model on a class of lattices or graphs for which there is a large degeneracy of the single particle ground states and where the projector onto the space of single particle ground states is highly reducible. This means that one can find a basis in the space of the single particle ground states such that the support of each single particle ground state belongs to some small cluster and these clusters do not overlap. We show how such lattices can be constructed in arbitrary dimensions. We construct all multi-particle ground states of these models for electron numbers not larger than the number of localized single particle eigenstates. We derive some of the ground state properties, esp. the residual entropy, i.e. the finite entropy density at zero temperature.