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

Physical Review Letters

Continuum limit of spin-1 chain

Takeo Inami, Satoru Odake

Published Mar 29, 1993• 7 citations
Publisher

Abstract

We study the continuum limit of the spin-1 chain in the non-Abelian bosonization approach of Affleck and show that the Hamiltonian of the integrable spin-1 chain yields the Lagrangian of the supersymmetric sine-Gordon model in the zero lattice spacing limit. We also show that the quantum group generators of the spin-1 chain give nonlocal charges of the supersymmetric sine-Gordon theory.

DOI
10.1103/physrevlett.70.2016

Related papers

Continuum Limit of Spin-1 Chain (the only change is added references)

Takeo Inami, Satoru Odake

We study the continuum limit of the spin-1 chain in the non-Abelian bosonization approach of Affleck and show that the Hamiltonian of integrable spin-1 chain yields the Lagrangian of supersymmetric sine-Gordon model in the zero lattice spacing limit. We also show that the quantum group generators of the spin-1 chain give non-local charges of the supersymmetric sine-Gordon theory.

arXiv:hep-th/9209019•Sep 7, 1992•0 citations

The continuum limit of the integrable open XYZ spin-1/2 chain

Tsukahara, H, Inami, T

We show that the continuum limit of the integrable XYZ spin-1/2 chain on a half-line gives rise to the boundary sine-Gordon theory using the perturbation method.

•Sep 7, 1998•0 citations

The Continuum Limit of the Integrable Open XYZ Spin-1/2 Chain

Hiroshi Tsukahara, Takeo Inami

We show that the continuum limit of the integrable XYZ spin-1/2 chain on a half-line gives rise to the boundary sine-Gordon theory using the perturbation method.

arXiv:hep-th/9809028•Journal of the Physical Society of Japan•Feb 15, 1999•0 citations

Finite size effects in the spin-1 XXZ and supersymmetric sine-Gordon models

Changrim Ahn, Rafael I. Nepomechie, Junji Suzuki

Starting from the Bethe Ansatz solution of the open integrable spin-1 XXZ quantum spin chain with diagonal boundary terms, we derive a set of nonlinear integral equations (NLIEs), which we propose to describe the boundary supersymmetric sine-Gordon model BSSG${}^{+}$ with Dirichlet boundary conditions on a finite interval. We compute the corresponding boundary $S$ matrix, and find that it coincides with the one proposed by Bajnok, Palla and Tak\\'acs for the Dirichlet BSSG${}^{+}$ model. We derive a relation between the (UV) parameters in the boundary conditions and the (IR) parameters in the boundary $S$ matrix. By computing the boundary vacuum energy, we determine a previously unknown parameter in the scattering theory. We solve the NLIEs numerically for intermediate values of the interval length, and find agreement with our analytical result for the effective central charge in the UV limit and with boundary conformal perturbation theory.

•Nov 13, 2006•0 citations

Quantum sine-Gordon thermodynamics: The Bethe ansatz method

Michael Fowler, X. Zotos

We show that the thermodynamic properties of the quantum sine-Gordon system in the zero-charge sector can be found from the appropriate limit of the Takahashi-Suzuki Bethe ansatz analysis of the $\mathrm{XYZ}$ spin chain. We prove that the rather complex criteria for allowed states in thermodynamic sums in that analysis correspond simply to including only states with normalizable wave functions. The behavior of the $\mathrm{XYZ}$ phase-shift function in the sine-Gordon limit is discussed.

Physical review. B, Condensed matter•Sep 1, 1981•74 citations

Continuum limit of sine-Gordon and φ4 chains by use of an effective potential

R. Giachetti, V. Tognetti, Ruggero Vaia

The effective potential previously introduced by the variational method is used to calculate thermodynamic quantities of quantum one-dimensional nonlinear fields in the weak-coupling approximation. The correct continuum limit is recovered both for integrable (sine-Gordon) and noninte- grable (${\ensuremath{\varphi}}^{4}$) models. Good agreement is found with exact Bethe-ansatz results for the specific heat.

Physical Review A•Aug 1, 1988•21 citations
We study the continuum limit of the spin-1 chain in the non-Abelian bosonization approach of Affleck and show that the Hamiltonian of the integrable spin-1 chain yields the Lagrangian of the supersymmetric sine-Gordon model in the zero lattice spacing limit. We also show that the quantum group generators of the spin-1 chain give nonlocal charges of the supersymmetric sine-Gordon theory.
Starting from the Bethe Ansatz solution of the open integrable spin-1 XXZ quantum spin chain with diagonal boundary terms, we derive a set of nonlinear integral equations (NLIEs), which we propose to describe the boundary supersymmetric sine-Gordon model BSSG+{}^{+}+ with Dirichlet boundary conditions on a finite interval. We compute the corresponding boundary SSS matrix, and find that it coincides with the one proposed by Bajnok, Palla and Tak\\'acs for the Dirichlet BSSG+{}^{+}+ model. We derive a relation between the (UV) parameters in the boundary conditions and the (IR) parameters in the boundary SSS matrix. By computing the boundary vacuum energy, we determine a previously unknown parameter in the scattering theory. We solve the NLIEs numerically for intermediate values of the interval length, and find agreement with our analytical result for the effective central charge in the UV limit and with boundary conformal perturbation theory.
We show that the thermodynamic properties of the quantum sine-Gordon system in the zero-charge sector can be found from the appropriate limit of the Takahashi-Suzuki Bethe ansatz analysis of the XYZ\mathrm{XYZ}XYZ spin chain. We prove that the rather complex criteria for allowed states in thermodynamic sums in that analysis correspond simply to including only states with normalizable wave functions. The behavior of the XYZ\mathrm{XYZ}XYZ phase-shift function in the sine-Gordon limit is discussed.