THE SAWTOOTH CHAIN: FROM HEISENBERG SPINS TO HUBBARD ELECTRONS

摘要

We report on recent studies of the spin-half Heisenberg and the Hubbard model onthe sawtooth chain. For both models we construct a class of exact eigenstates whichare localized due to the frustrating geometry of the lattice for a certain relation of theexchange (hopping) integrals. Although these eigenstates differ in details for the twomodels because of the different statistics, they share some characteristic features. Thelocalized eigenstates are highly degenerate and become ground states in high magneticfields (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 calcu-lated exactly by a mapping of the manifold of localized ground states onto a classicalhard-dimer problem, and explicit expressions for thermodynamic quantities can be de-rived which are valid at low temperatures near the saturation field for the Heisenbergmodel or around a certain value of the chemical potential for the Hubbard model, re-spectively.