Entropy of fermionic models on highly frustrated lattices

TL;DR

This paper investigates the entropy and localized states of spinless fermions on highly frustrated lattices with flat bands, revealing significant zero-temperature entropy and cooling effects, with implications for related Hubbard models.

Contribution

It provides a detailed analysis of localized states and entropy in flat-band fermionic models, extending insights to the Hubbard model and flat-band ferromagnetism.

Findings

Finite zero-temperature entropy at specific chemical potentials

Strong cooling effects during adiabatic chemical potential changes

Localized states are key to understanding the entropy and thermodynamics

Abstract

Spinless fermions on highly frustrated lattices are characterized by a lowest single-particle band which is completely flat. Concrete realizations are provided by the sawtooth chain and the kagome lattice. For these models a real-space picture is given in terms of localized states. Furthermore, we find a finite zero-temperature entropy for a suitable choice of the chemical potential. The entropy is computed numerically at finite temperature and one observes a strong cooling effect during adiabatic changes of the chemical potential. We argue that the localized states, the associated zero-temperature entropy and thus also the large temperature variations carry over to the repulsive Hubbard model. The relation to flat-band ferromagnetism is also discussed briefly.