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Modern Physics Letters A

WEAK-COUPLING PHASE DIAGRAM OF THE ONE-DIMENSIONAL DEFORMED T-J MODEL

QINGSHAN MA, Jianhui Dai, Zhaoxin Xu, Jun Zhang

Published Mar 28, 2007• 1 citation
Publisher

Abstract

The deformed t-J lattice model is defined by replacing the fermion operators by the deformed Hubbard operators in the t-term but without changing the J-term in the conventional t-J model. The physics of this model was argued to be continuously connected to those of the t-J one when the deformation parameter λ varies from zero to unit. In this paper, by using the bosonization field theory and renormalization group technique, we study the phase diagram of the one dimension deformed t-J model in the regime where λ and J/t are both positively small but comparable to each other. By explicitly incorporating the contributions from the deformation-induced six-particle term and the antiferromagnetic exchange interaction, we find that at half-filling the system shows three distinct ground states characterized by the Luttinger liquid, the spin-density-wave and the bond-order-wave, respectively. These results indicate that the ground state phases of the deformed t-J model is neither connected smoothly to those of the system at λ = 1 nor to those of the conventional t-J model.

DOI
10.1142/s021773230702333x

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The deformed t-J lattice model is defined by replacing the fermion operators by the deformed Hubbard operators in the t-term but without changing the J-term in the conventional t-J model. The physics of this model was argued to be continuously connected to those of the t-J one when the deformation parameter λ varies from zero to unit. In this paper, by using the bosonization field theory and renormalization group technique, we study the phase diagram of the one dimension deformed t-J model in the regime where λ and J/t are both positively small but comparable to each other. By explicitly incorporating the contributions from the deformation-induced six-particle term and the antiferromagnetic exchange interaction, we find that at half-filling the system shows three distinct ground states characterized by the Luttinger liquid, the spin-density-wave and the bond-order-wave, respectively. These results indicate that the ground state phases of the deformed t-J model is neither connected smoothly to those of the system at λ = 1 nor to those of the conventional t-J model.
In this paper, we study the phase diagram of the one-dimensional deformed t–J1–J2 model with frustrated exchange interaction. The introduction of the deformed parameter ζ softens the strength of the induced four- and six-electron interactions caused by the no-double occupancy constraint. For the small ζ and in the weak-coupling regime, we use the bosonization approach and the renormalization group techniques to obtain the phase diagram, which is characterized by the singlet-(SS) and triplet-superconducting (TS), spin-density-wave (SDW) as well as bond-charge-density wave (BCDW) instabilities. The TS and BCDW phases are realized in the whole regime while the SDW and SS correlations depend on J2/J1 < (J2/J1)c or J2/J1 > (J2/J1)c, where (J2/J1)c = 1/3. Furthermore, the deformed model with ζ ≪ 1 is expected to adiabatically connect to the conventional t–J1–J2 model with ζ = 1.
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.
By using the bosonization approach and the renormalization group (RG) technique, we study the half-filled band one-dimensional t–U–J model with additional on-bond repulsion (W>0) in the weak-coupling regime. The presence of on-bond repulsion is responsible for realization of a metallic phase in the system, and the phase diagram is strongly controlled by the symmetry of the model. By analyzing the RG flow diagram and comparing order parameters, the phase boundaries are determined and the structure of the phase diagram is clarified. In the case of SU (2) ⊗ SU (2) symmetry, the phase diagram consists of a metallic phase characterized by a Luttinger liquid (LL) and two insulting phases characterized by the degenerate spin-density-wave (SDW) and the bond-charge-density-wave (BCDW). In the SU (2) ⊗ U(1)-symmetric case, the phase diagram contains two metallic phases: a LL and a Luther–Emery phase, and three insulating phases: the transverse SDW ( SDW ±), the longitudinal SDW ( SDW z) and the dimerized BCDW. The insulating charge-density-wave and bond-spin-density-wave (BSDW) phases are always suppressed in the ground state. In addition, the system show a long-ranged order in the BCDW and SDW z phases.
By using the bosonization approach and renormalization group analysis,we study the ground state phase diagram of one-dimensional extended Hubbard model at half-filling in the regime where U and V are both positive but less than t, finding that the system shows three distinct ground states characterized by the spin-density-wave,the charge-density-wave and the bond-charge-density-wave,respectively.These results demonstrate that the ground state phases of the extended Hubbard model are not identical with those of the conventional Hubbard model.
We present an analytic study of the phase diagram of the one-dimensional $t\ensuremath{-}J$ model and a couple of its cousins. To deal with the interactions induced by the no double occupancy constraints, we introduce a deformation of the Hubbard operators. When the deformation parameter $\ensuremath{\Delta}$ is small, the induced interactions are softened, accessible by perturbation theory. We combine bosonization with renormalization group techniques to map out the phase diagram of the system. We argue that when $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\Delta}}1,$ there is no essential change in the phase diagram. A comparison with the existing results in the literature obtained by other methods justifies our deformation approach.
We study the phase diagram of a one-dimensional extended Hubbard model with antiferromagnetic exchange interaction analytically and numerically. The bosonization and transfer-matrix renormalization group methods are used in the corresponding coupling regimes. At half-filling, the system is a Mott insulator with a finite spin excitation gap if the on-site Coulomb repulsion is fairly smaller than the antiferromagnetic exchange JJJ. This Mott insulator is characterized by the bond-charge-density-wave order or spontaneously dimerization. In the weak-coupling regime where the spin-charge separation holds approximately, the critical point separating the gapless and gapped spin liquid phases is ${U}_{c}\ensuremath{\sim}J∕2$. However, as JJJ increases, the spin-charge couplings become important and the critical point Uc{U}_{c}Uc​ is significantly suppressed and eventually tends to zero as $J\ensuremath{\rightarrow}\ensuremath{\infty}$. Away from half-filling, the charge gap completely collapses but the spin gap persists.