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

arXiv:cond-mat/0204299 · Physical review. B, Condensed matter

One-dimensional behavior and sliding Luttinger liquid phase in a frustrated spin- 12 crossed chain model: Contribution of exact diagonalizations

Philippe Sindzingre, J.-B. Fouet, C. Lhuillier

Published Nov 15, 2002• 39 citations
arXivHTMLPDF

Abstract

Exact diagonalizations indicate that the effective one-dimensional behavior (sliding Luttinger liquid phase) of the frustrated spin-1/2 crossed chain model, predicted by Starykh, Singh, and Levine [Phys. Rev. Lett. 88, 167203 (2002)], persists for a wide range of interchain couplings. The extension of the other phases (plaquette valence bond crystal and N\'eel long-range order) is made precise. The coexistence region of these two phases, proposed by Sachdev and Park [Ann. Phys. (N.Y.) 298, 58 (2002)], has at most a very narrow width.

DOI
10.1103/physrevb.66.174424

Related papers

1-Dimensional behavior and sliding Luttinger liquid phase in a frustrated spin-1/2 crossed chain model: contribution of exact diagonalizations

Philippe Sindzingre, J.-B. Fouet, C. Lhuillier

Exact diagonalizations indicate that the effective 1-dimensional behavior (sliding Luttinger liquid phase) of the frustrated spin-1/2 crossed chain model, predicted by Starykh, Singh and Levine [Phys. Rev. Lett. 88, 167203 (2002)], persists for a wide range of transverse couplings. The extension of the other phases (plaquette valence bond crystal and Néel long range order) is precised. No clear indication of a coexistence of these two phases is found, at variance with a suggestion of Sachdev and Park (cond-mat/0108214).

•Jan 1, 2002•0 citations

Spin-1/2 frustrated antiferromagnet on a spatially anisotopic square lattice: contribution of exact diagonalizations

Philippe Sindzingre

The phase diagram of a spin-1/2 $J-J'-J_2$ model is investigated by means of exact diagonalizations on finite samples. This model is a generalization of the $J_1-J_2$ model on the square lattice with two different nearest-neighbor couplings $J,J'$ and may be also viewed as an array of coupled Heisenberg chains. The results suggest that the resonnating valence bond state predicted by Nersesyan and Tsvelik [Phys. Rev. B {\bf 67}, 024422 (2003)] for $J_2=0.5J' \ll J$ is realized and extends beyond the limit of small interchain coupling along a curve nearly coincident with the line where the energy per spin is maximum. This line is likely bordered on both side by a columnar dimer long range order. This columnar order could extends for $J'\to J$ which correspond to the $J_1-J_2$ model.

•Jan 1, 2004•0 citations

Spinons in a Crossed-Chains Model of a 2D Spin Liquid

Oleg A. Starykh, Rajiv R. P. Singh, Gregory Levine

Using the random phase approximation, we show that a crossed-chains model of spin-1/2 Heisenberg chains with frustrated interchain couplings has a nondimerized spin-liquid ground state in 2D, with deconfined spinons as the elementary excitations. The results are confirmed by a bosonization study, which shows that the system is an example of a "sliding Luttinger liquid." In an external field, the system develops an incommensurate field-induced long-range order with a finite transition temperature.

arXiv:cond-mat/0106260•Physical Review Letters•Apr 4, 2002•46 citations

Spin-1/2 frustrated antiferromagnet on a spatially anisotropic square lattice: Contribution of exact diagonalizations

Philippe Sindzingre

The phase diagram of a spin-1/2 $J\ensuremath{-}{J}^{\ensuremath{'}}\ensuremath{-}{J}_{2}$ model is investigated by means of exact diagonalizations on finite samples. This model is a generalization of the ${J}_{1}--{J}_{2}$ model on the square lattice with two different nearest-neighbor couplings ${J,J}^{\ensuremath{'}}$ and may also be viewed as an array of coupled Heisenberg chains. The results suggest that the resonating valence bond state predicted by Nersesyan and Tsvelik [Phys. Rev. B 67, 024422 (2003)] for ${J}_{2}{=0.5J}^{\ensuremath{'}}\ensuremath{\ll}J$ is realized and extends beyond the limit of small interchain coupling along a curve nearly coincident with the line where the energy per spin is maximum. This line is likely bordered on both sides by a columnar dimer long range order. This columnar order could extend for ${J}^{\ensuremath{'}}\ensuremath{\rightarrow}J$ which correspond to the ${J}_{1}--{J}_{2}$ model.

arXiv:cond-mat/0307118•Physical Review B•Mar 19, 2004•46 citations

Exact diagonalization studies of two-dimensional frustrated anti-ferromagnet models

C. Lhuillier, Philippe Sindzingre, J.-B. Fouet

We describe the four kinds of behavior found in two-dimensional isotropic quantum anti-ferromagnets. Two of them display long-range order at T = 0: the Néel state and the valence bond crystal. The last two are spin liquids. Properties of these different states are briefly described and open questions are underlined. PACS Nos.: 75.10Jm, 75.50Ee, 75.40-s

arXiv:cond-mat/0009336•Canadian Journal of Physics•Jan 1, 2001•19 citations

Sliding Luttinger liquid phases

Ranjan Mukhopadhyay, C. L. Kane, T. C. Lubensky

We study systems of coupled spin-gapped and gapless Luttinger liquids. First, we establish the existence of a sliding Luttinger liquid phase for a system of weakly coupled parallel quantum wires, with and without disorder. It is shown that the coupling can stabilize a Luttinger liquid phase in the presence of disorder. We then extend our analysis to a system of crossed Luttinger liquids and establish the stability of a non-Fermi-liquid state: the crossed sliding Luttinger liquid phase. In this phase the system exhibits a finite-temperature, long-wavelength, isotropic electric conductivity that diverges as a power law in temperature T as $\stackrel{\ensuremath{\rightarrow}}{T}0.$ This two-dimensional system has many properties of a true isotropic Luttinger liquid, though at zero temperature it becomes anisotropic. An extension of this model to a three-dimensional stack exhibits a much higher in-plane conductivity than the conductivity in a perpendicular direction.

arXiv:cond-mat/0102163•Physical review. B, Condensed matter•Jul 9, 2001•131 citations
Exact diagonalizations indicate that the effective one-dimensional behavior (sliding Luttinger liquid phase) of the frustrated spin-1/2 crossed chain model, predicted by Starykh, Singh, and Levine [Phys. Rev. Lett. 88, 167203 (2002)], persists for a wide range of interchain couplings. The extension of the other phases (plaquette valence bond crystal and N'eel long-range order) is made precise. The coexistence region of these two phases, proposed by Sachdev and Park [Ann. Phys. (N.Y.) 298, 58 (2002)], has at most a very narrow width.
Exact diagonalizations indicate that the effective 1-dimensional behavior (sliding Luttinger liquid phase) of the frustrated spin-1/2 crossed chain model, predicted by Starykh, Singh and Levine [Phys. Rev. Lett. 88, 167203 (2002)], persists for a wide range of transverse couplings. The extension of the other phases (plaquette valence bond crystal and Néel long range order) is precised. No clear indication of a coexistence of these two phases is found, at variance with a suggestion of Sachdev and Park (cond-mat/0108214).
The phase diagram of a spin-1/2 J−J′−J2J-J'-J_2J−J′−J2​ model is investigated by means of exact diagonalizations on finite samples. This model is a generalization of the J1−J2J_1-J_2J1​−J2​ model on the square lattice with two different nearest-neighbor couplings J,J′J,J'J,J′ and may be also viewed as an array of coupled Heisenberg chains. The results suggest that the resonnating valence bond state predicted by Nersesyan and Tsvelik [Phys. Rev. B {\bf 67}, 024422 (2003)] for J2=0.5J′≪JJ_2=0.5J' \ll JJ2​=0.5J′≪J is realized and extends beyond the limit of small interchain coupling along a curve nearly coincident with the line where the energy per spin is maximum. This line is likely bordered on both side by a columnar dimer long range order. This columnar order could extends for J′→JJ'\to JJ′→J which correspond to the J1−J2J_1-J_2J1​−J2​ model.
Using the random phase approximation, we show that a crossed-chains model of spin-1/2 Heisenberg chains with frustrated interchain couplings has a nondimerized spin-liquid ground state in 2D, with deconfined spinons as the elementary excitations. The results are confirmed by a bosonization study, which shows that the system is an example of a "sliding Luttinger liquid." In an external field, the system develops an incommensurate field-induced long-range order with a finite transition temperature.
The phase diagram of a spin-1/2 $J\ensuremath{-}{J}^{\ensuremath{'}}\ensuremath{-}{J}_{2}$ model is investigated by means of exact diagonalizations on finite samples. This model is a generalization of the J1−−J2{J}_{1}--{J}_{2}J1​−−J2​ model on the square lattice with two different nearest-neighbor couplings ${J,J}^{\ensuremath{'}}$ and may also be viewed as an array of coupled Heisenberg chains. The results suggest that the resonating valence bond state predicted by Nersesyan and Tsvelik [Phys. Rev. B 67, 024422 (2003)] for ${J}_{2}{=0.5J}^{\ensuremath{'}}\ensuremath{\ll}J$ is realized and extends beyond the limit of small interchain coupling along a curve nearly coincident with the line where the energy per spin is maximum. This line is likely bordered on both sides by a columnar dimer long range order. This columnar order could extend for ${J}^{\ensuremath{'}}\ensuremath{\rightarrow}J$ which correspond to the J1−−J2{J}_{1}--{J}_{2}J1​−−J2​ model.
We study systems of coupled spin-gapped and gapless Luttinger liquids. First, we establish the existence of a sliding Luttinger liquid phase for a system of weakly coupled parallel quantum wires, with and without disorder. It is shown that the coupling can stabilize a Luttinger liquid phase in the presence of disorder. We then extend our analysis to a system of crossed Luttinger liquids and establish the stability of a non-Fermi-liquid state: the crossed sliding Luttinger liquid phase. In this phase the system exhibits a finite-temperature, long-wavelength, isotropic electric conductivity that diverges as a power law in temperature T as $\stackrel{\ensuremath{\rightarrow}}{T}0.$ This two-dimensional system has many properties of a true isotropic Luttinger liquid, though at zero temperature it becomes anisotropic. An extension of this model to a three-dimensional stack exhibits a much higher in-plane conductivity than the conductivity in a perpendicular direction.