Exactly solvable dimerized XXZ Heisenberg chain

Igor Karnaukhov

National Academy of Sciences Kiev

The spin-1/2 XXZ Heisenberg chain with dimerized exchange integrals is proposed and solved exactly by means of the Bethe ansatz method. We discuss a specific example of an inhomogeneous spin-1/2 XXZ Heisenberg chain, the simples dimerized model with spin XX $J_j=J(-1)^{j}$ and ZZ $\Delta_j = \Delta (-1)^{j}$ exchange integrals. The model Hamiltonian is reduced to two noninteracting XXZ Heisenberg chains with equaled in magnitude but opposite in sign interactions. The phase state of the model is defined by two spinless fermion subbands with different interactions: repulsive ('antiferromagnetic') into one and attractive ('ferromagnetic') with the same strength into another. The subbands are connected via the constraint according to which the total spin or the total number of spinless fermions is conserved.