In this paper we present for the first time the exact solution in the narrow-band limit of the 1D extended Hubbard model with nearest-neighbour spin-spin interactions described by an exchange constant J. An external magnetic field h is also taken int
o account. This result has been obtained in the framework of the Greens functions formalism, using the Composite Operator Method. By means of this theoretical background, we have studied some relevant features such as double occupancy, magnetization, spin-spin and charge-charge correlation functions and derived a phase diagram for both ferro (J>0) and anti-ferro (J<0) coupling in the limit of zero temperature. We also report a study on density of states, specific heat, charge and spin susceptibilities. In the limit of zero temperature, we show that the model exhibits a very rich phase diagram characterized by different magnetic orders and by the coexistence of charge and spin orderings at commensurate filling. Moreover, our analysis at finite temperature of density of states and response functions shows the presence of low-temperature charge and spin excitations near the phase boundaries.
By using Density Matrix Renormalization Group (DMRG) technique we study the 1D extended anisotropic Heisenberg model. We find that starting from the ferromagnetic phase, the system undergoes two quantum phase transitions (QPTs) induced by frustration
. By increasing the next-nearest-neighbor (NNN) interaction, the ground state of the system changes smoothly from a completely polarized state to a NNN correlated one. On the contrary, letting the in-plane interaction to be greater than the out-of-plane one, the ground state changes abruptly.
