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/9811353 · Physical review. B, Condensed matter

Bifurcation at the c=3/2 Takhtajan-Babujian point to the c=1 critical line

Atsuhiro Kitazawa, K. Nomura

Published May 1, 1999• 17 citations
arXivHTMLPDF

Abstract

We study the $S=1$ quantum spin chains with bilinear, biquadratic, plus bond alternation in the vicinity of the $S=1$ Takhtajan-Babujian model. Transition line between the Haldane and the dimer phases is determined numerically. To see the crossover behavior from $c=3/2 [k=2$ SU(2) Weiss-Zumino-Witten (WZW) model] at the Takhtajan-Babujian point to $c=1 [k=1$ SU(2) WZW model], we calculate the conformal anomaly c and scaling dimensions of the primary fields on the transition line.

DOI
10.1103/physrevb.59.11358

Related papers

Conformal anomaly and critical exponents of the spin-1 Takhtajan-Babujian model

Francisco Castilho Alcaraz, Marcio Jose Martins

The authors consider the critical behaviour of the spin-1 Hamiltonian of the Takhtajan-Babujian model. The Bethe ansatz equations for this antiferromagnet in a finite chain are investigated analytically and numerically. The conformal anomaly and critical exponents are obtained by exploiting their relations with the eigenspectrum of the finite system. The results strongly support the conjecture that the Wess-Zumino-Witten non-linear sigma model with topological charge k=2 is the underlying field theory for this statistical mechanics model.

Journal of Physics A Mathematical and General•Apr 7, 1988•34 citations

Conformal invariance and critical exponents of the Takhtajan-Babujian models

Francisco Castilho Alcaraz, Marcio Jose Martins

The authors are concerned with the critical properties of antiferromagnetic Takhtajan-Babujian models with spin S=1, 3/2 and 2. The leading eigenenergies of this Hamiltonian, in a finite chain, are calculated by investigating numerically and analytically the Bethe ansatz equations for the finite system. The critical exponents and the conformal anomaly are obtained from their relations with the eigenspectrum of the finite Hamiltonian. The appearance of logarithmic corrections produces poor estimates. However, a combination of analytical and numerical methods produces very good estimates. Their results strongly support the conjecture that the Wess-Zumino-Witten-Novikov non-linear sigma models with topological charge k=2S are the underlying field theories for these spin-S statistical mechanics models.

Journal of Physics A Mathematical and General•Dec 7, 1988•45 citations

Isotropic spin-1 chain with twisted boundary condition

Gábor Fáth, Jenő Sólyom

The possible ground states and the phase transitions of a spin-1 chain with bilinear-biquadratic exchange are studied numerically. In order to see better the real asymptotic behavior of the infinite system and to determine the necessary degeneracies, a twisted boundary condition is used that reduces the finite-size effects. This calculation confirms that a second-order Ising-type phase transition occurs at the Takhtajan-Babujian point from the dimerized phase to the singlet Haldane phase. The transition at the Lai-Sutherland point, to a massless phase with three soft modes, is found to be of Kosterlitz-Thouless type.

Physical review. B, Condensed matter•Jan 1, 1993•73 citations

Isotropic spin-1 chains with bond alternation: analytic and numerical studies

Kiyohito Totsuka, Yoshihiro Nishiyama, Naomichi Hatano +1 more

Isotropic spin-1 chains with bond alternation are studied. Analytic (both variational and perturbative) results are presented. A phase transition is found to separate the S=1 Haldane phase and the dimer phase. The critical point is numerically determined using the Binder parameter. The universality class is predicted to be given by the level-1 SU(2) Wess-Zumin-Witten model, and this prediction is supported by the present exact diagonalization study. The dimer phase is found to be connected to the "S=2" Haldane phase in a special limit. The change of the excitation spectra and the string order parameter with bond alternation is discussed.

Journal of Physics Condensed Matter•Jun 19, 1995•67 citations

Bilinear-biquadratic spin-1 model in the Haldane and dimerized phases

Mykhailo V. Rakov, Michael Weyrauch

We study the low-lying spectrum of the bilinear-biquadratic Heisenberg model in the dimerized and Haldane phases using a tensor renormalization method. At the critical point $\ensuremath{\theta}=\ensuremath{-}\ensuremath{\pi}/4$, the finite-size spectrum predicted by the Wess-Zumino-Witten (WZW) model can only partly be confirmed. We find a singlet-singlet gap which does not fit into the WZW systematics. The results obtained are compared to Bethe ansatz, exact diagonalization, and density-matrix renormalization group calculations for specific parameters.

arXiv:2111.04561•Physical review. B./Physical review. B•Jan 31, 2022•5 citations

Dimerization transitions in spin-1 chains

Natalia Chepiga, Ian K. Affleck, Frédéric Mila

We study spontaneous dimerization transitions in a Heisenberg spin-1 chain with additional next-nearest-neighbor and three-site interactions using extensive numerical simulations and a conformal field-theory analysis. We show that the transition can be second order in the Wess-Zumino-Witten (WZW) $\mathrm{SU}{(2)}_{2}$ or Ising universality class, or first order. We argue that these features are generic because of a marginal operator in the WZW $\mathrm{SU}{(2)}_{2}$ model and because of two topologically distinct nondimerized phases with or without edge states. We also provide explicit numerical evidence of conformal towers of singlets inside the spin gap at the Ising transition. Implications for other models are briefly discussed.

arXiv:1603.01395•Physical review. B./Physical review. B•Jun 20, 2016•44 citations
We study the S=1S=1S=1 quantum spin chains with bilinear, biquadratic, plus bond alternation in the vicinity of the S=1S=1S=1 Takhtajan-Babujian model. Transition line between the Haldane and the dimer phases is determined numerically. To see the crossover behavior from c=3/2[k=2c=3/2 [k=2c=3/2[k=2 SU(2) Weiss-Zumino-Witten (WZW) model] at the Takhtajan-Babujian point to c=1[k=1c=1 [k=1c=1[k=1 SU(2) WZW model], we calculate the conformal anomaly c and scaling dimensions of the primary fields on the transition line.
The authors consider the critical behaviour of the spin-1 Hamiltonian of the Takhtajan-Babujian model. The Bethe ansatz equations for this antiferromagnet in a finite chain are investigated analytically and numerically. The conformal anomaly and critical exponents are obtained by exploiting their relations with the eigenspectrum of the finite system. The results strongly support the conjecture that the Wess-Zumino-Witten non-linear sigma model with topological charge k=2 is the underlying field theory for this statistical mechanics model.
The authors are concerned with the critical properties of antiferromagnetic Takhtajan-Babujian models with spin S=1, 3/2 and 2. The leading eigenenergies of this Hamiltonian, in a finite chain, are calculated by investigating numerically and analytically the Bethe ansatz equations for the finite system. The critical exponents and the conformal anomaly are obtained from their relations with the eigenspectrum of the finite Hamiltonian. The appearance of logarithmic corrections produces poor estimates. However, a combination of analytical and numerical methods produces very good estimates. Their results strongly support the conjecture that the Wess-Zumino-Witten-Novikov non-linear sigma models with topological charge k=2S are the underlying field theories for these spin-S statistical mechanics models.
The possible ground states and the phase transitions of a spin-1 chain with bilinear-biquadratic exchange are studied numerically. In order to see better the real asymptotic behavior of the infinite system and to determine the necessary degeneracies, a twisted boundary condition is used that reduces the finite-size effects. This calculation confirms that a second-order Ising-type phase transition occurs at the Takhtajan-Babujian point from the dimerized phase to the singlet Haldane phase. The transition at the Lai-Sutherland point, to a massless phase with three soft modes, is found to be of Kosterlitz-Thouless type.
Isotropic spin-1 chains with bond alternation are studied. Analytic (both variational and perturbative) results are presented. A phase transition is found to separate the S=1 Haldane phase and the dimer phase. The critical point is numerically determined using the Binder parameter. The universality class is predicted to be given by the level-1 SU(2) Wess-Zumin-Witten model, and this prediction is supported by the present exact diagonalization study. The dimer phase is found to be connected to the "S=2" Haldane phase in a special limit. The change of the excitation spectra and the string order parameter with bond alternation is discussed.
We study the low-lying spectrum of the bilinear-biquadratic Heisenberg model in the dimerized and Haldane phases using a tensor renormalization method. At the critical point $\ensuremath{\theta}=\ensuremath{-}\ensuremath{\pi}/4$, the finite-size spectrum predicted by the Wess-Zumino-Witten (WZW) model can only partly be confirmed. We find a singlet-singlet gap which does not fit into the WZW systematics. The results obtained are compared to Bethe ansatz, exact diagonalization, and density-matrix renormalization group calculations for specific parameters.
We study spontaneous dimerization transitions in a Heisenberg spin-1 chain with additional next-nearest-neighbor and three-site interactions using extensive numerical simulations and a conformal field-theory analysis. We show that the transition can be second order in the Wess-Zumino-Witten (WZW) SU(2)2\mathrm{SU}{(2)}_{2}SU(2)2​ or Ising universality class, or first order. We argue that these features are generic because of a marginal operator in the WZW SU(2)2\mathrm{SU}{(2)}_{2}SU(2)2​ model and because of two topologically distinct nondimerized phases with or without edge states. We also provide explicit numerical evidence of conformal towers of singlets inside the spin gap at the Ising transition. Implications for other models are briefly discussed.