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/9806369 · Physical review. B, Condensed matter

Chiral universality class in a frustrated three-leg spin ladder

P. Azaria, P. Lecheminant, A. A. Nersesyan

Published Oct 1, 1998• 25 citations
arXivHTMLPDF

Abstract

We study a model of three $S=1/2$ antiferromagnetic Heisenberg spin chains weakly coupled by on-rung and plaquette-diagonal interchain interactions. It is shown that the model exhibits a critical phase with central charge $C=2$ and belongs to the class of ``chirally stabilized'' liquids recently introduced by Andrei, Douglas, and Jerez. By allowing anisotropic interactions in spin space, we find an exact solution at a Toulouse point which captures all universal properties of the model, including the SU(2) symmetric case. At this critical point the massless degrees of freedom are described in terms of an effective $S=1/2$ Heisenberg spin chain and two critical Ising models. We discuss the spectral properties of the model, compute spin-spin correlation functions, and estimate the NMR relaxation rate.

DOI
10.1103/physrevb.58.r8881

Related papers

Chirally Stabilized Critical State in Marginally Coupled Spin Systems

P. Azaria, P. Lecheminant

We study a class of one-dimensional models consisting of a frustrated (N+1)-leg spin ladder, its asymmetric doped version as a special example of a Luttinger liquid in an active environment, and the N-channel Kondo-Heisenberg model away from half-filling. It is shown that these models exhibit a critical phase with generally a non-integer central charge and belong to the class of chirally stabilized spin liquids recently introduced by Andrei, Douglas, and Jerez [Phys. Rev. B 58, 7619 (1998)]. By allowing anisotropic interactions in spin space, an exact solution in the N=2 case is found at a Toulouse point which captures all universal properties of the models. At the critical point, the massless degrees of freedom are described in terms of an effective S=1/2 Heisenberg spin chain and two critical Ising models. The Toulouse limit solution enables us to discuss the spectral properties, the computation of the spin-spin correlation functions as well as the estimation of the NMR relaxation rate of the frustrated three-leg ladder. Finally, it is shown that the critical point becomes unstable upon switching on some weak backscattering perturbations in the frustrated three-leg ladder.

•Dec 22, 1999•0 citations

Ground-state phase diagram of a spin- 12 frustrated three-leg antiferromagnetic Heisenberg ladder

Xiaoqun Wang, Ningsheng Zhu, Changfeng Chen

Using the density matrix renormalization group method we have studied the ground-state phase diagram of a spin-1/2 frustrated three-leg antiferromagnetic Heisenberg ladder, and identified two phases corresponding to the spin-3/2 chain and the standard spin ladder. Varying the diagonal coupling ${J}_{\ifmmode\times\else\texttimes\fi{}}$ leads to a quantum phase transition from one ground state to the other, but does not alter the gapless nature of the excitation spectra. On the phase boundary, the degenerate ground states form a chiral spin liquid with a central charge $c=2.$ The critical value of ${J}_{\ifmmode\times\else\texttimes\fi{}}$ is insensitive to the number of legs in the ladder, suggesting that a quantum phase transition may occur at ${J}_{\ifmmode\times\else\texttimes\fi{}}=0.6$ for the isotropic spin-1/2 antiferromagnetic Heisenberg model on the square lattice.

Physical review. B, Condensed matter•Nov 15, 2002•11 citations

Ground state phase diagram of an S = 1 2 two-leg Heisenberg spin ladder system with negative four-spin interaction

Keigo Hijii, Tôru Sakai

We investigate the ground-state phase diagram and critical properties of the $S=1/2$ two-leg Heisenberg spin ladder system with a negative four-spin interaction using a numerical exact diagonalization method. Using the perturbation theory in the strong negative rung-coupling limit, we derive an $S=1$ bilinear-biquadratic chain as an effective model. We discuss the ground-state phase diagram in this limit. Next we numerically determine a phase boundary between the rung singlet phase and the columnar dimer (CD) phase by the phenomenological renormalization group method, and one between the CD phase and the Haldane phase by the twisted boundary condition method. We confirm that the phase transition between the CD phase and the Haldane phase is of second order and this universality class is described by the $k=2$ $SU(2)$ Wess-Zumino-Novikov-Witten nonlinear $\ensuremath{\sigma}$ model, calculating the central charge and scaling dimensions.

Physical Review B•Sep 4, 2013•8 citations

Composite pairings in chirally stabilized critical fluids

P. Azaria, P. Lecheminant

We study a one-dimensional electron gas in a special antiferromagnetic environment made by two spin-1/2 Heisenberg chains and a one-dimensional two-channel Kondo-Heisenberg lattice away from half-filling. These models flow to an intermediate fixed point which belongs to the universality class of chirally stabilized liquids. Using a Toulouse point approach, the universal properties of the models are determined as well as the identification of the leading instabilities. It is shown that these models exhibit a non-Fermi-liquid behavior with strong enhanced composite pairing correlations.

arXiv:cond-mat/0001072•Physical review. B, Condensed matter•Jul 1, 2000•7 citations

Groundstate Properties of Frustrated Spin Systems on a Ladder

匡良 塚野, Minoru Takahashi

A spin-1/2 Heisenberg model on a ladder, which consists of one ferromagnetic leg and one antiferromagnetic leg connected by antiferromagnetic rungs, is discussed. The phase transition in the groundstate is investigated in such a system. It is shown that the spontaneous magnetization, m , becomes zero if the interchain coupling R is larger than a critical value R c . It is found that R c =1.134461 ±0.000001 by the exact diagonalization. In the region R < R c , we also find that the spontaneous magnetization is proportional to \(\sqrt{R_{\rm c}-R}\) near the critical point R c . Moreover an exact eigenstate with the total spin S =0 is obtained.

Journal of the Physical Society of Japan•Apr 1, 1997•10 citations

Phase diagram of a spin-1/2 Heisenberg ladder with a chirality-chirality interaction

Matéo Fontaine, Shunsuke Furukawa

A spin-1/2 Heisenberg model with a chirality-chirality interaction (CCI) on a two-leg ladder provides a minimal setup to explore an interplay between spin and chirality degrees of freedom. This model is potentially relevant for understanding the effects of a four-spin ring exchange and a phonon-mediated interaction on a ladder. By applying the Abelian bosonization and two types of spin-chirality duality, we derive a comprehensive ground-state phase diagram that includes previously unexplored cases of a ferromagnetic rung exchange $J_\perp<0$ or a negative CCI $K_{\rm ch}<0$. The phase diagram consists of the rung singlet (RS) phase, the Haldane phase, and three non-magnetic ordered phases. Moreover, the RS and Haldane phases consist of several regions with different dominant correlations in terms of spin, dimer, or chirality. We perform numerical simulations to confirm the predicted phase structure and critical properties.

arXiv:2408.11731•Aug 21, 2024•0 citations
We study a model of three S=1/2S=1/2S=1/2 antiferromagnetic Heisenberg spin chains weakly coupled by on-rung and plaquette-diagonal interchain interactions. It is shown that the model exhibits a critical phase with central charge C=2C=2C=2 and belongs to the class of ``chirally stabilized'' liquids recently introduced by Andrei, Douglas, and Jerez. By allowing anisotropic interactions in spin space, we find an exact solution at a Toulouse point which captures all universal properties of the model, including the SU(2) symmetric case. At this critical point the massless degrees of freedom are described in terms of an effective S=1/2S=1/2S=1/2 Heisenberg spin chain and two critical Ising models. We discuss the spectral properties of the model, compute spin-spin correlation functions, and estimate the NMR relaxation rate.
We study a class of one-dimensional models consisting of a frustrated (N+1)-leg spin ladder, its asymmetric doped version as a special example of a Luttinger liquid in an active environment, and the N-channel Kondo-Heisenberg model away from half-filling. It is shown that these models exhibit a critical phase with generally a non-integer central charge and belong to the class of chirally stabilized spin liquids recently introduced by Andrei, Douglas, and Jerez [Phys. Rev. B 58, 7619 (1998)]. By allowing anisotropic interactions in spin space, an exact solution in the N=2 case is found at a Toulouse point which captures all universal properties of the models. At the critical point, the massless degrees of freedom are described in terms of an effective S=1/2 Heisenberg spin chain and two critical Ising models. The Toulouse limit solution enables us to discuss the spectral properties, the computation of the spin-spin correlation functions as well as the estimation of the NMR relaxation rate of the frustrated three-leg ladder. Finally, it is shown that the critical point becomes unstable upon switching on some weak backscattering perturbations in the frustrated three-leg ladder.
Using the density matrix renormalization group method we have studied the ground-state phase diagram of a spin-1/2 frustrated three-leg antiferromagnetic Heisenberg ladder, and identified two phases corresponding to the spin-3/2 chain and the standard spin ladder. Varying the diagonal coupling ${J}_{\ifmmode\times\else\texttimes\fi{}}$ leads to a quantum phase transition from one ground state to the other, but does not alter the gapless nature of the excitation spectra. On the phase boundary, the degenerate ground states form a chiral spin liquid with a central charge c=2.c=2.c=2. The critical value of ${J}_{\ifmmode\times\else\texttimes\fi{}}$ is insensitive to the number of legs in the ladder, suggesting that a quantum phase transition may occur at ${J}_{\ifmmode\times\else\texttimes\fi{}}=0.6$ for the isotropic spin-1/2 antiferromagnetic Heisenberg model on the square lattice.
We investigate the ground-state phase diagram and critical properties of the S=1/2S=1/2S=1/2 two-leg Heisenberg spin ladder system with a negative four-spin interaction using a numerical exact diagonalization method. Using the perturbation theory in the strong negative rung-coupling limit, we derive an S=1S=1S=1 bilinear-biquadratic chain as an effective model. We discuss the ground-state phase diagram in this limit. Next we numerically determine a phase boundary between the rung singlet phase and the columnar dimer (CD) phase by the phenomenological renormalization group method, and one between the CD phase and the Haldane phase by the twisted boundary condition method. We confirm that the phase transition between the CD phase and the Haldane phase is of second order and this universality class is described by the k=2k=2k=2 SU(2)SU(2)SU(2) Wess-Zumino-Novikov-Witten nonlinear $\ensuremath{\sigma}$ model, calculating the central charge and scaling dimensions.
We study a one-dimensional electron gas in a special antiferromagnetic environment made by two spin-1/2 Heisenberg chains and a one-dimensional two-channel Kondo-Heisenberg lattice away from half-filling. These models flow to an intermediate fixed point which belongs to the universality class of chirally stabilized liquids. Using a Toulouse point approach, the universal properties of the models are determined as well as the identification of the leading instabilities. It is shown that these models exhibit a non-Fermi-liquid behavior with strong enhanced composite pairing correlations.
A spin-1/2 Heisenberg model on a ladder, which consists of one ferromagnetic leg and one antiferromagnetic leg connected by antiferromagnetic rungs, is discussed. The phase transition in the groundstate is investigated in such a system. It is shown that the spontaneous magnetization, m , becomes zero if the interchain coupling R is larger than a critical value R c . It is found that R c =1.134461 ±0.000001 by the exact diagonalization. In the region R < R c , we also find that the spontaneous magnetization is proportional to Rc−R\sqrt{R_{\rm c}-R}Rc​−R​ near the critical point R c . Moreover an exact eigenstate with the total spin S =0 is obtained.
A spin-1/2 Heisenberg model with a chirality-chirality interaction (CCI) on a two-leg ladder provides a minimal setup to explore an interplay between spin and chirality degrees of freedom. This model is potentially relevant for understanding the effects of a four-spin ring exchange and a phonon-mediated interaction on a ladder. By applying the Abelian bosonization and two types of spin-chirality duality, we derive a comprehensive ground-state phase diagram that includes previously unexplored cases of a ferromagnetic rung exchange J⊥<0J_\perp<0J⊥​<0 or a negative CCI Kch<0K_{\rm ch}<0Kch​<0. The phase diagram consists of the rung singlet (RS) phase, the Haldane phase, and three non-magnetic ordered phases. Moreover, the RS and Haldane phases consist of several regions with different dominant correlations in terms of spin, dimer, or chirality. We perform numerical simulations to confirm the predicted phase structure and critical properties.