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Modern Physics Letters B

PHASE DIAGRAM OF ONE-DIMENSIONAL DEFORMED t–J1–J2 MODEL WITH FRUSTRATED EXCHANGE INTERACTION

Hanqin Ding, Jun Zhang

Published Jun 20, 2011• 1 citation
Publisher

Abstract

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.

DOI
10.1142/s0217984911026553

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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.
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.
Using the low-energy effective field theory scenario combined Abelian bosonization and renormalization-group techniques, we study the Hubbard chain with additional anisotropic nearest-neighbor and isotropic next-nearest-neighbor spin exchanges J and J′ in the weak-coupling regime. The spin correlations are non-critical due to the anisotropic J (Jxy ≠ Jz). The frustrating antiferromagnetic exchange J′ leads to an enhancement of the dimerized phase and induces a long-range charge-density-wave (CDW) phase. For smaller values of J′ (J′ < 2U/3), the quantum phase diagram consists of the insulating spin-density-wave ( SDW xy, SDW z) and bond-charge-density-wave (BCDW) phases and the triplet superconducting ( TS 0, TS ±) phase. For larger J′ (J′ ≥ 2U/3), a finite CDW phase appears. The result shows that the frustrated spin exchange J′ changes the topological structure of the usual t-U-J chain.
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 the bosonization and renormalization-group schemes, a half-filled Hubbard chain with density-dependent hopping is investigated at weak coupling. The model involved has an electron–hole symmetry and an SO(4) symmetry. The phase diagram consists of three different phases divided by a charge transition at on-site repulsion U = U c and a spin transition at U = U s , with U s = − U c = 16 π ( t c − 1 ) , including a Mott insulator with the SDW correlation, a dimerized insulator with the BCDW correlation, and a Luttinger metal with the coexisting TS and BSDW correlations. The effective three-body repulsion ( t c − 1 > 0 ) and attraction ( t c − 1 < 0 ) induce the dimerized and metallic phases, respectively. • We study a 1D Hubbard model with symmetric density-dependent hopping analytically. • We provide a theoretical scheme of realization of the BCDW and TS instabilities. • The results supplement further understanding of quantum properties of 1D correlated systems.
We use bosonization and renormalization group methods to determine the ground-state phase diagram of a one-dimensional frustrated Kondo-Heisenberg system consisting of a one-dimensional spin-12\frac{1}{2}21​ Luttinger liquid coupled by a Kondo exchange interaction JK{J}_{K}JK​ to a frustrated quantum antiferromagnetic Heisenberg chain, with a nearest-neighbor exchange coupling J1{J}_{1}J1​ and a next-nearest-neighbor (frustrating) exchange interaction J2{J}_{2}J2​. We analyze the interplay of quantum frustration in the antiferromagnetic chain with the Kondo exchange coupling JK{J}_{K}JK​ with the Luttinger liquid. We discuss the structure of the phase diagram of this system as a function of the ratios JK/J1{J}_{K}/{J}_{1}JK​/J1​, J2/J1{J}_{2}/{J}_{1}J2​/J1​, and of the parameters of the Luttinger liquid. In particular, we discuss in detail the regimes in which a pair-density-wave state may be realized and its relation with the spin correlations in the frustrated antiferromagnetic chain.