Low-temperature properties of the Hubbard model on highly frustrated one-dimensional lattices

TL;DR

This paper analyzes the low-temperature properties of the Hubbard model on frustrated one-dimensional lattices with flat bands, deriving exact ground states and thermodynamic behaviors, and confirming results with numerical methods.

Contribution

It provides a complete set of exact many-electron ground states and thermodynamic expressions for the Hubbard model on specific frustrated lattices, a novel analytical achievement.

Findings

Identification of exact ground states at low fillings

Derivation of closed-form thermodynamic quantities

Observation of residual entropy and magnetic properties

Abstract

We consider the repulsive Hubbard model on three highly frustrated one-dimensional lattices -- sawtooth chain and two kagom\'{e} chains -- with completely dispersionless (flat) lowest single-electron bands. We construct the complete manifold of {\em exact many-electron} ground states at low electron fillings and calculate the degeneracy of these states. As a result, we obtain closed-form expressions for low-temperature thermodynamic quantities around a particular value of the chemical potential $\mu_0$. We discuss specific features of thermodynamic quantities of these ground-state ensembles such as residual entropy, an extra low-temperature peak in the specific heat, and the existence of ferromagnetism and paramagnetism. We confirm our analytical results by comparison with exact diagonalization data for finite systems.