Correlators of the ladder spin model in the strong coupling limit. (English) Zbl 0980.82003

Abarenkova, N. I.; Izergin, A. G.; Pronko, A. G.

J. Math. Sci., New York 104, No. 3, 1087-1096 (2001) and Zap. Nauchn. Semin. POMI 251, 7-21 (1998).

From the introduction: The aim is to calculate the temperature and time-dependent correlation functions of the “ladder” spin model consisting of two Heisenberg \(XX0\text{ spin}-1/2\) chains interacting via the third local spin components in the limit of infinitely strong coupling. By means of the Jordan-Wigner transformation, the Hamiltonian of the ladder model can be transformed into the Hamiltonian of the Hubbard model. Thus, the relation between the ladder model and the Hubbard model is, in this sense, similar to the relation between the \(XX0\) Heisenberg chain and free fermions on the lattice. The expressions of the local spin operators are, however, nonlocal in terms of the local fermion operators. Thus, we calculate the matrix elements necessary for calculating correlator functions directly in terms of the local spin operators, similarly to the case of the simple \(XX0\) chain.

MSC:

82B20

Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics

Keywords:

ladder spin model; temperature; time-dependent correlation functions; Jordan-Wigner transformation