Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

International Journal of Modern Physics B

PHASE DIAGRAM OF THE ONE-DIMENSIONAL t–U–J MODEL WITH ON-BOND REPULSION AT HALF FILLING

Hanqin Ding, Yanshen Wang

Published Dec 30, 2010• 2 citations
Publisher

Abstract

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.

DOI
10.1142/s0217979210057651

Related papers

PHASE DIAGRAM OF ONE-DIMENSIONAL t–U–J MODEL WITH ANISOTROPIC ANTIFERROMAGNETIC EXCHANGE

Hanqin Ding, Yanshen Wang

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.

Modern Physics Letters B•Oct 11, 2010•12 citations

Phase diagram of the Hubbard chain with symmetric density-dependent hopping

Xin Sun, Weiting Chen, Hanqin Ding

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.

Results in Physics•Sep 23, 2024•1 citation

Theoretical investigation of four-body interaction in the one-dimensional extended Hubbard model

Weiting Chen, Hanqin Ding, Jun Zhang

In the weak-coupling regime, we analytically investigate phase diagram of a one-dimensional half-filled extended Hubbard model with nearest neighboring four-electron interaction (Q), in addition to the usual two-electron couplings (U,V>0). The additional four-electron coupling splits independent Gaussian and spin-gap transitions and also leads to the charge-gap transition. For the positive Q, the ground state exhibits three insulating phases, charge-density-wave (CDW), spin-density-wave (SDW) and bond-spin-density-wave (BSDW). For the negative Q, the phase diagram consists of five phases, which, besides the SDW and CDW phases, contain bond-charge-density-wave (BCDW), Luttinger liquid (LL) and Luther–Emery (LE) phases.

Results in Physics•Feb 2, 2022•3 citations

Phase Diagram of the One-Dimensional Extended Hubbard Model at Half Filling

Masahisa Tsuchiizu, Akira Furusaki

We reexamine the ground-state phase diagram of the one-dimensional half-filled Hubbard model with on-site and nearest-neighbor repulsive interactions. We calculate second-order corrections to coupling constants in the weak-coupling renormalization-group approach ( g-ology) to show that the bond-charge-density-wave (BCDW) phase exists for weak couplings in between the charge-density-wave (CDW) and spin-density-wave (SDW) phases. We find that the umklapp scattering of parallel-spin electrons destabilizes the BCDW state and gives rise to a bicritical point where the CDW-BCDW and SDW-BCDW continuous-transition lines merge into the CDW-SDW first-order transition line.

arXiv:cond-mat/0109051•Physical Review Letters•Jan 16, 2002•131 citations

Tricritical behavior in the extended Hubbard chains

Masaaki Nakamura

Phase diagrams of the one-dimensional extended Hubbard model (including nearest-neighbor interaction $V)$ at half- and quarter-filling are studied by observing level crossings of excitation spectra using the exact diagonalization. This method is based on the Tomonaga-Luttinger liquid theory including logarithmic corrections which stem from the renormalization of the Umklapp- and the backward-scattering effects. Using this approach, the phase boundaries are determined with high accuracy, and then the structure of the phase diagram is clarified. At half-filling, the phase diagram consists of two Berezinskii-Kosterlitz-Thouless (BKT) transition lines and one Gaussian transition line in the charge sector, and one spin-gap transition line. This structure reflects the $\mathrm{U}(1)\ensuremath{\bigotimes}\mathrm{SU}(2)$ symmetry of the electron system. Near the $U=2V$ line, the Gaussian and the spin-gap transitions take place independently from the weak- to the intermediate-coupling region, but these two transition lines are coupled in the strong-coupling region. This result demonstrates existence of a tricritical point and a bond-charge-density-wave (BCDW) phase between charge- and spin-density-wave (CDW, SDW) phases. To clarify this mechanism of the transition, we also investigate effect of a correlated hopping term, which plays a role to enlarge BCDW and bond-spin-density-wave (BSDW) phases. At quarter-filling, a similar crossover phenomenon also takes place in the large-$V$ region involving spin-gap and BKT-type metal-insulator transitions.

arXiv:cond-mat/9909277•Physical review. B, Condensed matter•Jun 15, 2000•230 citations

Ground-state phase diagram of the one-dimensional half-filled extended Hubbard model

Masahisa Tsuchiizu, Akira Furusaki

We revisit the ground-state phase diagram of the one-dimensional half-filled extended Hubbard model with on-site (U) and nearest-neighbor (V) repulsive interactions. In the first half of the paper, using the weak-coupling renormalization-group approach $(g$-ology) including second-order corrections to the coupling constants, we show that bond-charge-density-wave (BCDW) phase exists for $U\ensuremath{\approx}2V$ in between charge-density-wave (CDW) and spin-density-wave (SDW) phases. We find that the umklapp scattering of parallel-spin electrons disfavors the BCDW state and leads to a bicritical point where the CDW-BCDW and SDW-BCDW continuous-transition lines merge into the CDW-SDW first-order transition line. In the second half of the paper, we investigate the phase diagram of the extended Hubbard model with either additional staggered site potential $\ensuremath{\Delta}$ or bond alternation $\ensuremath{\delta}.$ Although the alternating site potential $\ensuremath{\Delta}$ strongly favors the CDW state (that is, a band insulator), the BCDW state is not destroyed completely and occupies a finite region in the phase diagram. Our result is a natural generalization of the work by Fabrizio, Gogolin, and Nersesyan [Phys. Rev. Lett. $83,$ 2014 (1999)], who predicted the existence of a spontaneously dimerized insulating state between a band insulator and a Mott insulator in the phase diagram of the ionic Hubbard model. The bond alternation $\ensuremath{\delta}$ destroys the SDW state and changes it into the BCDW state (or Peierls insulating state). As a result the phase diagram of the model with $\ensuremath{\delta}$ contains only a single critical line separating the Peierls insulator phase and the CDW phase. The addition of $\ensuremath{\Delta}$ or $\ensuremath{\delta}$ changes the universality class of the CDW-BCDW transition from the Gaussian transition into the Ising transition.

arXiv:cond-mat/0308157•Physical Review B•Jan 15, 2004•78 citations
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 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 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.
In the weak-coupling regime, we analytically investigate phase diagram of a one-dimensional half-filled extended Hubbard model with nearest neighboring four-electron interaction (Q), in addition to the usual two-electron couplings (U,V>0). The additional four-electron coupling splits independent Gaussian and spin-gap transitions and also leads to the charge-gap transition. For the positive Q, the ground state exhibits three insulating phases, charge-density-wave (CDW), spin-density-wave (SDW) and bond-spin-density-wave (BSDW). For the negative Q, the phase diagram consists of five phases, which, besides the SDW and CDW phases, contain bond-charge-density-wave (BCDW), Luttinger liquid (LL) and Luther–Emery (LE) phases.
We reexamine the ground-state phase diagram of the one-dimensional half-filled Hubbard model with on-site and nearest-neighbor repulsive interactions. We calculate second-order corrections to coupling constants in the weak-coupling renormalization-group approach ( g-ology) to show that the bond-charge-density-wave (BCDW) phase exists for weak couplings in between the charge-density-wave (CDW) and spin-density-wave (SDW) phases. We find that the umklapp scattering of parallel-spin electrons destabilizes the BCDW state and gives rise to a bicritical point where the CDW-BCDW and SDW-BCDW continuous-transition lines merge into the CDW-SDW first-order transition line.
Phase diagrams of the one-dimensional extended Hubbard model (including nearest-neighbor interaction V)V)V) at half- and quarter-filling are studied by observing level crossings of excitation spectra using the exact diagonalization. This method is based on the Tomonaga-Luttinger liquid theory including logarithmic corrections which stem from the renormalization of the Umklapp- and the backward-scattering effects. Using this approach, the phase boundaries are determined with high accuracy, and then the structure of the phase diagram is clarified. At half-filling, the phase diagram consists of two Berezinskii-Kosterlitz-Thouless (BKT) transition lines and one Gaussian transition line in the charge sector, and one spin-gap transition line. This structure reflects the $\mathrm{U}(1)\ensuremath{\bigotimes}\mathrm{SU}(2)$ symmetry of the electron system. Near the U=2VU=2VU=2V line, the Gaussian and the spin-gap transitions take place independently from the weak- to the intermediate-coupling region, but these two transition lines are coupled in the strong-coupling region. This result demonstrates existence of a tricritical point and a bond-charge-density-wave (BCDW) phase between charge- and spin-density-wave (CDW, SDW) phases. To clarify this mechanism of the transition, we also investigate effect of a correlated hopping term, which plays a role to enlarge BCDW and bond-spin-density-wave (BSDW) phases. At quarter-filling, a similar crossover phenomenon also takes place in the large-VVV region involving spin-gap and BKT-type metal-insulator transitions.
We revisit the ground-state phase diagram of the one-dimensional half-filled extended Hubbard model with on-site (U) and nearest-neighbor (V) repulsive interactions. In the first half of the paper, using the weak-coupling renormalization-group approach (g(g(g-ology) including second-order corrections to the coupling constants, we show that bond-charge-density-wave (BCDW) phase exists for $U\ensuremath{\approx}2V$ in between charge-density-wave (CDW) and spin-density-wave (SDW) phases. We find that the umklapp scattering of parallel-spin electrons disfavors the BCDW state and leads to a bicritical point where the CDW-BCDW and SDW-BCDW continuous-transition lines merge into the CDW-SDW first-order transition line. In the second half of the paper, we investigate the phase diagram of the extended Hubbard model with either additional staggered site potential $\ensuremath{\Delta}$ or bond alternation $\ensuremath{\delta}.$ Although the alternating site potential $\ensuremath{\Delta}$ strongly favors the CDW state (that is, a band insulator), the BCDW state is not destroyed completely and occupies a finite region in the phase diagram. Our result is a natural generalization of the work by Fabrizio, Gogolin, and Nersesyan [Phys. Rev. Lett. 83,83,83, 2014 (1999)], who predicted the existence of a spontaneously dimerized insulating state between a band insulator and a Mott insulator in the phase diagram of the ionic Hubbard model. The bond alternation $\ensuremath{\delta}$ destroys the SDW state and changes it into the BCDW state (or Peierls insulating state). As a result the phase diagram of the model with $\ensuremath{\delta}$ contains only a single critical line separating the Peierls insulator phase and the CDW phase. The addition of $\ensuremath{\Delta}$ or $\ensuremath{\delta}$ changes the universality class of the CDW-BCDW transition from the Gaussian transition into the Ising transition.