arXiv:hep-th/9209019

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

Takeo Inami, Satoru Odake

Published Sep 7, 1992• 0 citations

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 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.

DOI: 10.48550/arxiv.hep-th/9209019

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arXiv:hep-th/9209019

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

Takeo Inami, Satoru Odake

Published Sep 7, 1992• 0 citations

arXiv HTML PDF

Abstract

DOI: 10.48550/arxiv.hep-th/9209019

Related papers

Continuum limit of spin-1 chain

Takeo Inami, Satoru Odake

Physical Review LettersMar 29, 19937 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/9809028Journal of the Physical Society of JapanFeb 15, 19990 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, 19980 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.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.

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Boundary non-local charges from the open spin chain

Anastasia Doikou

The N site open XXZ quantum spin chain with a right non-diagonal boundary and special diagonal left boundary is considered. The boundary non-local charges originally obtained from a field theoretical viewpoint, for the sine Gordon model on the half line, are recovered from the spin chain point of view. Furthermore, the symmetry of the open spin chain is exhibited. More specifically, we show that certain non–local charges commute with the transfer matrix of the open spin chain, depending on the choice of boundary conditions. In addition, we show explicitly that for a special choice of the left boundary, one of the non–local charges, in a particular representation, commutes with each one of the generators of the blob algebra, and hence with the corresponding local Hamiltonian. LAPTH-1029/04 Quantum groups have attracted much interest recently because of their intrinsic mathematical interest [1]–[3], but also because they provide a powerful scheme for deriving solutions of the Yang-Baxter equation [4]–[6] R12(λ1 − λ2) R13(λ1) R23(λ2) = R23(λ2) R13(λ1) R12(λ1 − λ2). (1.1) R acts on V ⊗2, whereas the Yang–Baxter equation on V ⊗3, and as customary R12 = R ⊗ I, R23 = I ⊗ R. TheThe N site open XXZ quantum spin chain with a right non-diagonal boundary and special diagonal left boundary is considered. The boundary non-local charges originally obtained from a field theoretical viewpoint, for the sine Gordon model on the half line, are recovered from the spin chain point of view. Furthermore, the symmetry of the open spin chain is exhibited. More specifically, we show that certain non–local charges commute with the transfer matrix of the open spin chain, depending on the choice of boundary conditions. In addition, we show explicitly that for a special choice of the left boundary, one of the non–local charges, in a particular representation, commutes with each one of the generators of the blob algebra, and hence with the corresponding local Hamiltonian. LAPTH-1029/04 Quantum groups have attracted much interest recently because of their intrinsic mathematical interest [1]–[3], but also because they provide a powerful scheme for deriving solutions of the Yang-Baxter equation [4]–[6] R12(λ1 − λ2) R13(λ1) R23(λ2) = R23(λ2) R13(λ1) R12(λ1 − λ2). (1.1) R acts on V ⊗2, whereas the Yang–Baxter equation on V ⊗3, and as customary R12 = R ⊗ I, R23 = I ⊗ R. The

Sep 14, 201318 citations

Boundary non-local charges from the open spin chain

Anastasia Doikou

arXiv:math-ph/0402067Journal of Statistical Mechanics Theory and ExperimentDec 7, 200522 citations

{}^{+}

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.