THE SAWTOOTH CHAIN: FROM HEISENBERG SPINS TO HUBBARD ELECTRONS

Stefano Bellucci A, Vadim Ohanyan

Taras Hutak, Taras Krokhmalskii, Oleg Derzhko +1 more

Jonas Richter, Oleg Derzhko, A. Honecker

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.

Б. И. Садовников, Наталья Германовна Иноземцева, V. I. Inozemtsev

The thermodynamics of an inhomogeneous 1D Heisenberg chain with alternating classical and quantum spins is studied. The explicit expressions for the free energy, specific heat, thermal spin correlations and linear susceptibility are found.

Carlo Heissenberg, Augusto Sagnotti

T. Schneider, E. Stoll