Abstract. We calculate the magnetic phase diagram of the Hubbard model for a Bethe lattice with nearest neighbour (NN) hopping t1 and next nearest neighbour (NNN) hopping t2 in the limit of infinite coordination. We use the amplitude t2/t1 of
We calculate the magnetic phase diagram of the Hubbard model for a Bethe lattice with nearest-neighbour (NN) hopping t 1 and next-nearest-neighbour (NNN) hopping t 2 in the limit of infinite coordination. We use the amplitude t 2 / t 1 of the NNN hopping to tune the density of states (DOS) of the non-interacting system from a situation with particle–hole symmetry to an asymmetric one with van-Hove singularities at the lower ( t 2 / t 1 >0) respectively upper ( t 2 / t 1 <0) band edge for large enough | t 2 / t 1 |. For this strongly asymmetric situation, we find rather extended parameter regions with ferromagnetic states and regions with antiferromagnetic states.
Ferromagnetism in the one-dimensional Hubbard model with the next-nearest-neighbor hopping is explored by using the exact-diagonalization method in a small cluster and the equation-of-motion method in the thermodynamic limit with electron density n = 3/2. With these two complementary methods, it is found that an intermediate value of the next-nearest-neighbor hopping amplitude t1 tends to stabilize the fully polarized ferromagnetic state under the condition that the on-site coulomb interaction U is sufficiently large in our model. The ground-state phase diagram of the model is presented in the t1—U plane.
The Hubbard model has attracted considerable interest due to its prototypical role in describing strongly interacting electronic systems, such as high-critical-temperature superconductors as well as many novel quantum materials. By introducing next-nearest-neighbor (NNN) hoppings to the Hubbard model, the phase diagram becomes richer, and fascinating phenomena arise in both, one-dimensional chains and square lattices, such as: antiferromagnetism, ferromagnetism, superconductivity (SC), as well as charge orders, among others. Moreover, NNN hoppings play a fundamental role in understanding effects of doping on magnetism and pairing orders in strongly interacting regimes. In this article, we review the recent progress in understanding the different competing phases of this model in one and two dimensions from a computational perspective. We comment on the pressing technical challenges, illustrate the controversial results concerning the emergence of the SC phase, and conclude with our perspectives on future explorations.
The ground-state phase diagram of two-dimensional Falicov-Kimball model with nearest-neighbour and next-nearest-neighbour hoppings (characterized by t,t' constants, respectively) has been studied in perturbative regime, i.e. in the case when on-site Coulomb interaction constant U is much larger than t,t' ones. The fourth-order phase diagram exhibits a rich structure, more complicated than for the ordinary Falicov-Kimball model. Possible experimental implications of the presence of nnn term are shortly discussed.
The paramagnetic phase diagram of the Hubbard model with nearest-neighbor and next-nearest-neighbor (NNN) hopping on the Bethe lattice is computed at half-filling and in the weakly doped regime using the self-energy functional approach for dynamical mean-field theory. NNN hopping breaks the particle-hole symmetry and leads to a strong asymmetry of the electron-doped and hole-doped regimes. Phase separation occurs at and near half-filling, and the critical temperature of the Mott transition is strongly suppressed.