Low-temperature thermodynamics of one class of flat-band models

TL;DR

This paper analyzes the low-temperature thermodynamics of flat-band frustrated lattice models, deriving exact ground states and thermodynamic expressions, validated by numerical data, for antiferromagnetic and Hubbard models.

Contribution

It provides exact solutions for many-particle ground states and thermodynamic properties of flat-band models, a novel analytical approach for these frustrated systems.

Findings

Exact many-particle ground states constructed

Closed-form expressions for thermodynamic quantities derived

Numerical data confirms analytical results

Abstract

We consider the antiferromagnetic Heisenberg model and the repulsive Hubbard model for a class of frustrated lattices with a completely dispersionless (flat) lowest one-particle (either one-magnon or one-electron) band. We construct exact many-particle ground states for a wide range of particle densities, calculate their degeneracy, and, as a result, obtain closed-form expressions for the low-temperature thermodynamic quantities around a particular value of the magnetic field $h_{\rm{sat}}$ or the chemical potential $\mu_0$. We confirm our analytic findings by numerical data for finite lattices.