Localized states on triangular traps and low-temperature properties of the antiferromagnetic Heisenberg and repulsive Hubbard models

TL;DR

This paper investigates localized states in antiferromagnetic Heisenberg and Hubbard models on one-dimensional lattices, analyzing their impact on ground-state degeneracy, thermodynamics, and low-temperature properties, including effects of perturbations.

Contribution

It introduces a detailed analysis of localized states on triangular traps and their influence on low-temperature behavior, including degeneracy lifting and effective spin models.

Findings

Localized states cause residual entropy and additional low-temperature peaks in specific heat.

Degeneracy due to localized states can be lifted by extra interactions, affecting thermodynamic properties.

Effective spin-1/2 transverse XX chain describes low-energy degrees of freedom after degeneracy lifting.

Abstract

We consider the antiferromagnetic Heisenberg and the repulsive Hubbard model on two $N$-site one-dimensional lattices, which support dispersionless one-particle states corresponding to localized states on triangular trapping cells. We calculate the degeneracy of the ground states in the subspaces with $n\le n_{\max}$, $n_{\max}\propto N$ magnons or electrons as well as the contribution of these states (independent localized states) to thermodynamic quantities. Moreover, we discuss another class of low-lying eigenstates (so-called interacting localized states) and calculate their contribution to the partition function. We also discuss the effect of extra interactions, which lift the degeneracy present due to the chirality of the localized states on triangles. The localized states set an extra low-energy scale in the system and lead to a nonzero residual ground-state entropy and to one (or more) additional low-temperature peak(s) in the specific heat. Low-energy degrees of freedom in the presence of perturbations removing degeneracy owing to the chirality can be described in terms of an effective (pseudo)spin-1/2 transverse $XX$ chain.