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An exact solvable model of the coupled identical XY spin chains interacting via the spin-ZZ exchange interaction between nearest-neighbor spins on different chains is proposed and solved by the means of the Bethe ansatz. We consider two identical chains in zigzag fashion, so that each site j is adjacent to the sites j+(-)1/2 on the other chain. Due to the Jordan-Wigner transformation, the Heisenberg model of coupled spin-1/2 chains is equivalent to the coupled free degenerated chains of spinless fermions with the density-density interaction on the nearest-neighbor lattice sites J. The model is quite elegant generalization of the well-known spin-1/2 XXZ Heisenberg chain to coupled spin chains. The phase separation state of cold fermionic atoms trapped in optical lattices cannot be described in the framework of the traditional one-dimensional Hubbard with a positive on-site interaction or Heisenberg models. We give a detailed analysis of the exact zero-temperature phase diagram in the case of the ferromagnetic interaction between chains. The phase state of the model is defined by the strength of the interaction J and the band filling of the chains of spinless fermions or an external magnetic field for the coupled Heisenberg chains. It is shown that the phase transition between the ferromagnetic at J<-4 and antiferromagnetic at -1.15 |
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