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

Abstract

We consider the repulsive Hubbard model on three highly frustrated one-dimensional lattices -- sawtooth chain and two kagomé 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 $μ_0$. 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.

20 pages, 12 figures, 2 tables