The sawtooth chain: From Heisenberg spins to Hubbard electrons

TL;DR

This paper explores localized eigenstates in the sawtooth chain for Heisenberg and Hubbard models, revealing their impact on ground-state degeneracy, thermodynamics, and specific heat, with exact solutions derived via a classical mapping.

Contribution

It introduces a class of exact localized eigenstates for both models on the sawtooth chain, linking their degeneracy and thermodynamics through a classical hard-dimer mapping.

Findings

Localized eigenstates are highly degenerate and influence low-temperature thermodynamics.

Exact expressions for thermodynamic quantities are derived near saturation fields and specific chemical potentials.

Localized states lead to an extra low-temperature maximum in the specific heat.

Abstract

We report on recent studies of the spin-half Heisenberg and the Hubbard model on the sawtooth chain. For both models we construct a class of exact eigenstates which are localized due to the frustrating geometry of the lattice for a certain relation of the exchange (hopping) integrals. Although these eigenstates differ in details for the two models because of the different statistics, they share some characteristic features. The localized eigenstates are highly degenerate and become ground states in high magnetic fields (Heisenberg model) or at certain electron fillings (Hubbard model), respectively. They may dominate the low-temperature thermodynamics and lead to an extra low-temperature maximum in the specific heat. The ground-state degeneracy can be calculated exactly by a mapping of the manifold of localized ground states onto a classical hard-dimer problem, and explicit expressions for thermodynamic quantities can be derived which are valid at low temperatures near the saturation field for the Heisenberg model or around a certain value of the chemical potential for the Hubbard model, respectively.