We examine extended bound states in a dilute limit of the extended Hubbard model on the two-dimensional square lattice.By solving exactly the two-body problem we have determined the binding energies, mobilities, and dispersion curves across the Brillouin zone for bound states of various symmetries.It turns out that the d-wave pairing is strongly favored by the nnn hopping and the intersite local pairs can have small effective masses, even in the case of strong binding.We have also found a possibility of extended S-d2-2 mixing of the bound states.
We consider an extended Hubbard model of interacting fermions on a lattice. The fermion kinetic energy corresponds to a tight-binding Hamiltonian with nearest-neighbor (-t) and next-nearest-neighbor (
t∣IH) hopping matrix elements. In addition to the on-site Hubbard interaction (U) we also consider a nearest-neighbor repulsion (V). We obtain the zero-temperature phase diagram of our model within the Hartree-Fock approximation. We consider ground states having charge- and spin-density-wave ordering as well as states with orbital antiferromagnetism or spin nematic order. The latter two states correspond to particle-hole binding with ${\mathrm{d}}_{{\mathrm{x}}^{2}\mathrm{\ensuremath{-}}{\mathrm{y}}^{2}}$ symmetry in the charge and spin channels, respectively. For
t∣IH=0, only the charge-density-wave and spin-density-wave states are energetically stable. For nonzero
t∣IH, we find that orbital antiferromagnetism (or spin nematic) order is stable over a finite portion of the phase diagram at weak coupling. This region of stability is seen to grow with increasing values of
t∣IH.
The attractive Hubbard model plays a paradigmatic role in the study of superconductivity (superfluidity) and has become directly realizable in ultracold atom experiments on optical lattices. However, the critical temperatures,
Tc's, remain lower than the lowest temperatures currently achievable in experiments. Here, we explore a possible route to enhance
Tc by introducing an additional next-nearest-neighbor (NNN) hopping,
t′, in a two-dimensional square lattice. We perform sign-problem-free determinant quantum Monte Carlo simulations to compute response functions such as pairing correlation functions, superfluid density, and uniform spin susceptibility. Our results show that a judicious choice of
t′ can increase
Tc by up to
50% compared to the case with only nearest-neighbor hopping. In contrast, the preformed pairs temperature scale, named pairing temperature,
Tp, decreases with increasing
∣t′/t∣, which should represent a reduction of the pseudogap region, favoring a more BCS-like behavior at intermediate coupling. We further analyze the interacting density of states to characterize the transition from a pseudogap regime to a fully gapped superconducting state. These findings suggest that NNN hopping could be a viable route to increase
Tc to values closer to experimentally accessible temperature scales.
Abstract The properties of the bound states on a lattice is an interesting problem related to the properties of superconductivity and Bose–Einstein condensation in a given model. By means of the exact solution of the Schrödinger equation the properties of the bound pairs on a frustrated, triangular lattice are examined within extended Hubbard model. Dispersion curves and mobilities are calculated for both positive and negative sign of the hopping integral. The possibility of increasing the mobility with increasing intersite Coulomb interaction is found. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)