We have used exact diagonalization and quantum Monte Carlo methods to study the one-dimensional t-J model including the three-site hopping term derived from the strong-coupling limit of the Hubbard model. The three-site term may be important to superconducting correlations since it allows direct hopping of local singlet electron pairs. The phase diagram is determined for several values of the strength of the three-site term and compared with that of the t-J and Hubbard models. Phase separation, which exists in the t-J model, is suppressed. In the low electron density region the formation of local singlet electron pairs is enhanced, leading to stronger superconducting correlations even for values J/t2. A large spin gap region extends from low electron densities up to high densities. In the low hole density region the superconducting correlations are suppressed at J/t>2.8 in spite of enhanced pair formation. This is because the three-site term, while enhancing the formation of electron pairs, leads to a repulsion between holes.
The $t\ensuremath{-}J$ model is a standard model of strongly correlated electrons, often studied in the context of high-
Tc superconductivity. However, most studies of this model neglect three-site terms, which appear at the same order as the superexchange
J. As these terms correspond to pair hopping, they are expected to play an important role in the physics of superconductivity when doped sufficiently far from half filling. We present a density matrix renormalization-group study of the one-dimensional $t\ensuremath{-}J$ model with the pair hopping terms included. We demonstrate that these additional terms radically change the one-dimensional ground-state phase diagram, extending the superconducting region at low fillings, while at larger fillings, superconductivity is completely suppressed. We explain this effect by introducing a simplified effective model of repulsive hardcore bosons.
We study the t-J model in one and two dimensions. It is shown that superconducting correlations at large distances are enhanced at doping 〈n〉=1/2, and near the region of phase separation. Including a nearest-neighbor density-density repulsion term of strength V, and working at large V/t and J/t, our results can be explained using a previously discussed variational state where electrons are paired in singlets without cluster formation, in analogy to the attractive Hubbard model. We argue that the physics of the t-J-V model is basically independent of the dimension and that a smooth connection exists between small and large V/t. Then, we conjecture that the two-dimensional t-J model should also present strong superconducting correlations near the region of phase separation, at 〈n〉\ensuremath{\sim}1/2. Numerical results both in one and two dimensions support our claims.
Our previous mean-field study concerning superconducting pairings in the extended Hubbard model with on-site repulsive and intersite attractive interaction and arbitrary electron density is extended to include the effects of nearest-neighbor exchange (
J) and correlated hopping (
K) interaction. Detailed numerical analysis of
s-,
p-, and
d-wave pairing solutions is performed for the two-dimensional square lattice with nearest- (
t) and next-nearest- (
t2) neighbor hopping, and the resulting mutual stability phase diagrams are given as a function of band filling and the interaction parameters. Antiferromagnetic exchange can enhance both the
d-wave and the extended
s-wave pairing. If it prevails over the repulsive intersite density-density interaction, such a term can be a leading mechanism for superconductivity. However, its effects strongly depend on the band filling and the
tt2 ratio, giving in particular for
t2=0 s-wave (
d-wave) pairing as most favorable in the low (high) density limit, but increasing
t2 can even reverse this tendency. The correlated hopping term which breaks the electron-hole symmetry affects
s-wave pairing mostly. A condensation transition (phase separation), possible in the presence of the attractive density-density interaction, is also analyzed within the random-phase approximation, and stability conditions of such an electron droplet phase with respect to other types of ordering are determined as a function of the band filling for the two-dimensional square lattice.
The t-J Hamiltonian is one of the cornerstones in the theoretical study of strongly correlated copper-oxide based materials. Using the density-matrix renormalization group method we obtain the phase diagram of the one-dimensional t-J chain in the presence of a periodic hopping modulation, as a prototype of coupled-segment models. While in the uniform 1D t-J model the near half-filling superconducting state dominates only at unphysically large values of the exchange coupling constant J/t>3; we show that a small hopping and exchange modulation very strongly reduces the critical coupling to be as low as J/t∼1/3--well within the physical regime. The phase diagram as a function of the electron filling also exhibits metallic, insulating line phases and regions of phase separation. We suggest that a superconducting state is easily stabilized if t-J segments creating local spin-singlet pairing are coupled to each other--another example is the ladder system.
The phase diagram of the one-dimensional t-J model is investigated by analyzing the results of exact diagonalization and the exact solutions at J/t=0 and 2. Phase separation takes place above a critical value of J around
Jc/t=2.5--3.5 depending on the electron density. In the small-J region, Tomonaga-Luttinger liquid theory holds and its correlation exponents are calculated as a function of J/t and the electron density. Superconducting correlations become dominant in a region between the solvable case (J/t=2) and phase separation. A spin-gap region is also found at low density.