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 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.
We numerically investigate the ground state of the extended $t\text{\ensuremath{-}}J$ Hamiltonian with periodic local modulations in one dimension by using the density-matrix renormalization group method. Examining charge and spin excitation gaps, as well as the pair binding energy, with extrapolated results to the thermodynamic limit, we obtain a rich ground-state phase diagram consisting of the metallic state, the superconducting state, the phase separation, and insulating states at commensurate fillings. Compared to the homogeneous one-dimensional (1D) $t\text{\ensuremath{-}}J$ model, the superconductivity is greatly enhanced and stabilized by the flat-band structure. This superconducting state in periodically modulated chains shares similar properties with ladder systems: significant negative pair binding energy occurs, and the singlet-pairing correlation function dominates with the algebraic decay while the single-particle Green's function and spin correlation function decay exponentially. On the other hand, the superlattice structure leads to nontrivial topological nature in insulating states, characterized by different integer Chern numbers at different fillings. Due to the interplay among the topology, the interaction, and the 1D confinement, gapless edge modes show strong spin-charge separation and in different regions can relate to different collective modes, which are the charge of a single fermion, the magnon, and the singlet pair. We also find two interaction-driven topological transitions: (i) at particle filling $\ensuremath{\rho}=\frac{1}{2}$, the low-energy edge excitations change from the magnon to singlet pair, accompanied with pair formation in bulk; and (ii) at $\ensuremath{\rho}=\frac{3}{4}$, while the gapless edge mode is always the charge of a single fermion, there is a gap-closing point and a $\ensuremath{\pi}$-phase shift in the quasiparticle spectrum.
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.
By using the field-theoretical techniques combining bosonization with renormalization group, we study a one-dimensional (1D) model of interacting electrons with on-site repulsion (U > 0), nearest-neighbor (nn) exchange (J) and correlated-hopping (t2, t3) interactions at weak coupling. In the case of a half-filled band, the two-body interaction t2 does not influence phase diagram of the model, while the presence of three-body interaction t3 makes the physics of the system highly non-trivial. By a Hartree–Fock decoupling, the effects of t3 bring about hopping of pairs, V-like (nn Coulomb interaction) and isotropic exchange terms in the reduced model Hamiltonian. Interestingly, a negative t3 provides a possibility for the occurrence of the triplet superconductivity in 1D system with purely repulsive interactions (U, J > 0). The ground state phase diagram including the insulating and superconducting phases is discussed analytically.
Phase diagram of the one dimensional t1−t2−J model: Ferromagnetism, triplet pairing, charge and pair density waves
We present a density matrix renormalization group (DMRG) study of an extended t−J model with hopping to the first and second neighbors -- the one dimensional t1−t2−J model. The full phase diagram as a function of the density n and exchange strength J, for both positive and negative values of t2, is obtained. For t2=−0.5 we observe that, in the strongly interacting region, Nagaoka Ferromagnetism (FM) is accompanied by a triplet pair density wave (PDW) upon doping. As the spin exchange J increases, a charge density wave (CDW) phase emerges and then gives way to singlet superconductivity (SC). This phase behaves as a singlet PDW with vanishing spacial average of the order parameter and a spin gap. When t2=0.5, the physics is basically reminiscent of the conventional t−J model, undergoing a transition from a metallic to a SC phase as a function of J.
We present a density matrix renormalization group study of an extended $t\text{\ensuremath{-}}J$ model with hopping to the first and second neighbors---the one-dimensional ${t}_{1}\text{\ensuremath{-}}{t}_{2}\text{\ensuremath{-}}J$ model. The full phase diagram as a function of the density n and exchange strength J, for both positive and negative values of t2, is obtained. For ${t}_{2}=\ensuremath{-}0.5$ we observe that, in the strongly interacting region, Nagaoka ferromagnetism is accompanied by a triplet pair density wave (PDW) upon doping. As the spin exchange J increases, a charge density wave phase emerges and then gives way to singlet superconductivity (SC). This phase behaves as a singlet PDW with vanishing spacial average of the order parameter and a spin gap. When t2=0.5, the physics is basically reminiscent of the conventional $t\text{\ensuremath{-}}J$ model, undergoing a transition from a metallic to a SC phase as a function of J.
We study signatures of superconductivity in a two-leg ``checkerboard'' Hubbard ladder model, defined as a one-dimensional (period 2) array of square plaquettes with an intraplaquette hopping t and interplaquette hopping ${t}^{\ensuremath{'}}$, using the density-matrix renormalization-group method. The highest pairing scale (characterized by the spin gap or the pair binding energy, extrapolated to the thermodynamic limit) is found for doping levels close to half-filling, $U\ensuremath{\approx}6t$ and ${t}^{\ensuremath{'}}/t\ensuremath{\approx}0.6$. Other forms of modulated hopping parameters, with periods of either one or three lattice constants, are also found to enhance pairing relative to the uniform two-leg ladder, although to a lesser degree. A calculation of the phase stiffness of the ladder reveals that in the regime with the strongest pairing, the energy scale associated with phase ordering is comparable to the pairing scale.