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

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.