Low-temperature thermodynamics for a flat-band ferromagnet: Rigorous versus numerical results

TL;DR

This paper analyzes the low-temperature thermodynamics of a flat-band ferromagnet modeled by the Hubbard model on a sawtooth chain, providing exact ground states, analytical thermodynamic expressions, and comparison with numerical data.

Contribution

It constructs exact many-electron ground states for the flat-band Hubbard model and maps the problem to a classical dimer model, deriving analytical thermodynamic results.

Findings

Exact ground states up to 1/4 filling

Analytical expressions for thermodynamic quantities

Low-temperature specific heat peak

Abstract

The repulsive Hubbard model on a sawtooth chain exhibits a lowest single-electron band which is completely dispersionless (flat) for a specific choice of the hopping parameters. We construct exact many-electron ground states for electron fillings up to 1/4. We map the low-energy degrees of freedom of the electron model to a model of classical hard dimers on a chain and, as a result, obtain the ground-state degeneracy as well as closed-form expressions for the low-temperature thermodynamic quantities around a particular value of the chemical potential. We compare our analytical findings with complementary numerical data. Although we consider a specific model, we believe that some of our results like a low-temperature peak in the specific heat are generic for flat-band ferromagnets.