In this paper we study the ground state phase diagram of a one-dimensional t-J-U model away from half-filling. In the large-bandwidth limit and for ferromagnetic exchange with easy-plane anisotropy a phase with gapless charge and massive spin excitations, characterized by the coexistence of triplet superconducting and spin density wave instabilities is realized in the ground state. With increasing ferromagnetic exchange transitions into a ferrometallic and then a spin gapped triplet superconducting phase take place.
In this paper we study the ground state phase diagram of a one-dimensional t-J-U model away from half-filling. In the large-bandwidth limit and for ferromagnetic exchange with easy-plane anisotropy a phase with gapless charge and massive spin excitations, characterized by the coexistence of triplet superconducting and spin density wave instabilities is realized in the ground state. With increasing ferromagnetic exchange transitions into a ferrometallic and then a spin gapped triplet superconducting phase take place.
In this paper we study the ground-state phase diagram of a one-dimensional $t\ensuremath{-}U\ensuremath{-}J$ model, at half-filling. In the large-bandwidth limit and for ferromagnetic exchange with easy-plane anisotropy, a phase with gapless charge and massive spin excitations, characterized by the coexistence of triplet superconducting and spin density wave instabilities is realized in the ground state. With reduction of the bandwidth, a transition into an insulating phase showing properties of the spin-21XY model takes place. In the case of weakly anisotropic antiferromagnetic exchange the system shows a long-range dimerized (Peierls) ordering in the ground state. The complete weak-coupling phase diagram of the model, including effects of the on-site Hubbard interaction, is obtained.
By using the bosonization approach and the weak-coupling renormalization group (RG) techniques, we study the phase diagram of one-dimensional half-filled t–U–J model parametrized by exchange anisotropy λ (0 ≤ λ ≤ 2) in the weak-coupling regime. In the case of anisotropic antiferromagnetic exchange (J > 0) and on-site repulsion (U > 0), the ground state is characterized by the spin-density-wave (SDW) and bond-charge-density-wave (BCDW) insulating phases. We identify the SDW correlation corresponding to the transverse SDW± phases with a gapless spin excitation (Δs=0) for λ < 4/3 and to the longitudinal SDWz phase with a spin gap (Δs > 0) for λ > 4/3, respectively. The charge excitation is always gapped (Δc > 0) in the whole regime, and the BCDW and SDWz phases show a long-range order. We also examine effects of the nonlocal Umklapp scattering of parallel-spin electrons, which play a role to weaken the BCDW phase and to enhance the SDW phase slightly. The results demonstrate that the properties of our model are not identical with those of the conventional t–U–J model.
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.
In the present work the numerical density matrix renormalization group (DMRG) algorithm is used to analyze the ground state properties of the Hubbard model with transverse spin-exchange. The DMRG algorithm, which was developed by White in 1992, is based on the following simple but effective concept: the ground-state wavefunction as well as the low energy excitations of a large interacting chain are obtained by increasing the lattice size iteratively, starting with a small one that can be diagonalized exactly. The exponentially growing Hilbert space is controlled by a renormalization procedure in which 'less important' degrees of freedom are integrated out. Motivated by recent experimental findings showing evidence for the competition or even coexistence of triplet superconductivity and ferromagnetism we focused our investigations on a rather simple extension of the Hubbard model including transverse spin exchange between electrons on nearest-neighbour sites. In the half-filled case, we showed that the phase diagram obtained in the weak-coupling limit has to be modified. A new phase, described by spin and charge excitation gap, shows long-range order in the longitudinal spin correlation, whereas superconducting correlations are surpressed and decay exponentially as expected for the case of a finite charge gap. In general, the presence of a repulsive on-site Coulomb interaction U leads to an enlargement of the sectors with nonvanishing charge gap at the expense of the sectors with spin gap. We extend our analysis to the case of a quarter-filled band. Depending on the value J/t the model belongs either to a gapless excitation phase or to a spin gapped phase with gapless charge degrees of freedom.
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 studied ferromagnetism in the one-dimensional Hubbard model with doubly degenerate atomic orbitals by means of the density-matrix renormalization-group method and obtained the ground-state phase diagrams. It was found that ferromagnetism is stable from low to high (0<n<1.75) electron density when the interactions are sufficiently strong. The quasi-long-range order of triplet superconductivity coexists with the ferromagnetic order for a strong Hund coupling region, where the interorbital interaction ${U}^{\ensuremath{'}}\ensuremath{-}J$ is attractive. At quarter-filling (n=1), the insulating ferromagnetic state appears, accompanying orbital quasi-long-range order. For low densities (n<1), ferromagnetism occurs owing to the ferromagnetic exchange interaction caused by virtual hoppings of electrons, the same as in the quarter-filled system. This comes from separation of the charge and spin-orbital degrees of freedom in the strong-coupling limit. This ferromagnetism is fragile against variation of band structure. For high densities (n>1), the phase diagram of the ferromagnetic phase is similar to that obtained in infinite dimensions. In this case, the double exchange mechanism is operative for stabilizing the ferromagnetic order and this long-range order is robust against variation of the band dispersion. A partially polarized state appears in the density region $1.68\ensuremath{\lesssim}n\ensuremath{\lesssim}1.75$ and phase separation occurs for n just below the half-filling (n=2).