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arXiv:cond-mat/0205444 · Physical review. B, Condensed matter

Deformed Hubbard operator, bosonization, and phase diagram of the one-dimensional t−J model

Guang‐Hong Chen, Yong-Shi Wu

Published Oct 23, 2002• 14 citations
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Abstract

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.

DOI
10.1103/physrevb.66.155111

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We present an analytic study of the phase diagram of the one-dimensional t\ensuremath−Jt\ensuremath{-}Jt\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 \ensuremathΔ\ensuremath{\Delta}\ensuremathΔ 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 \ensuremathΔ\ensuremath→1,\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\Delta}}1,\ensuremathΔ\ensuremath→​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.
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.
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.
We use the density-matrix renormalization group to study the one-dimensional bosonic Hubbard model, with and without disorder. We obtain the gaps in all phases, certain correlation functions, and the superfluid density. A finite-size-scaling analysis enables us to obtain an accurate phase diagram and the $\ensuremath{\beta}$ function at the superfluid--Mott insulator transition and the Kosterlitz-Thouless essential singularity in the pure case. We also obtain coupling constants used in effective field theories for this system.
The zero-temperature phase diagram of the one-dimensional Bose-Hubbard model with nearest-neighbor interaction is investigated using the density-matrix renormalization group. Recently normal phases without long-range order have been conjectured between the charge-density wave phase and the superfluid phase in one-dimensional bosonic systems without disorder. Our calculations demonstrate that there is no intermediate phase in the one-dimensional Bose-Hubbard model but a simultaneous vanishing of crystalline order and appearance of superfluid order. The complete phase diagrams with and without nearest-neighbor interaction are obtained. Both phase diagrams show reentrance from the superfluid phase to the insulator phase.
The ground-state phase diagram of the one-dimensional asymmetric Hubbard model at half-filling is studied by means of a perturbation expansion in the large-U limit and White's density matrix renormalization-group method for various values of the couplings. We argue that the introduction of asymmetry in the hopping parameters is a relevant perturbation for any repulsive U and drives the system into an ordered N\'eel antiferromagnet. The transition belongs to the Kosterlitz-Thouless universality class.