Q-operator and T-Q relation from the fusion hierarchy

Wen Li Yang; Rafael I. Nepomechie; Yao Zhong Zhang

doi:10.1016/j.physletb.2005.12.022

Q-operator and T-Q relation from the fusion hierarchy

Wen Li Yang, Rafael I. Nepomechie, Yao Zhong Zhang

Physics

Research output: Contribution to journal › Article › peer-review

68 Scopus citations

Abstract

We propose that the Baxter Q-operator for the spin-1/2 XXZ quantum spin chain is given by the j→∞ limit of the transfer matrix with spin-j (i.e., (2j+1)-dimensional) auxiliary space. Applying this observation to the open chain with general (non-diagonal) integrable boundary terms, we obtain from the fusion hierarchy the T-Q relation for generic values (i.e., not roots of unity) of the bulk anisotropy parameter. We use this relation to determine the Bethe ansatz solution of the eigenvalues of the fundamental transfer matrix. This approach is complementary to the one used recently to solve the same model for the roots of unity case.

Original language	English (US)
Pages (from-to)	664-670
Number of pages	7
Journal	Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
Volume	633
Issue number	4-5
DOIs	https://doi.org/10.1016/j.physletb.2005.12.022
State	Published - Feb 16 2006

Keywords

Bethe ansatz
Fusion hierarchy
Q-operator
Reflection equation
Spin chain

ASJC Scopus subject areas

Nuclear and High Energy Physics

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10.1016/j.physletb.2005.12.022

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title = "Q-operator and T-Q relation from the fusion hierarchy",

abstract = "We propose that the Baxter Q-operator for the spin-1/2 XXZ quantum spin chain is given by the j→∞ limit of the transfer matrix with spin-j (i.e., (2j+1)-dimensional) auxiliary space. Applying this observation to the open chain with general (non-diagonal) integrable boundary terms, we obtain from the fusion hierarchy the T-Q relation for generic values (i.e., not roots of unity) of the bulk anisotropy parameter. We use this relation to determine the Bethe ansatz solution of the eigenvalues of the fundamental transfer matrix. This approach is complementary to the one used recently to solve the same model for the roots of unity case.",

keywords = "Bethe ansatz, Fusion hierarchy, Q-operator, Reflection equation, Spin chain",

author = "Yang, {Wen Li} and Nepomechie, {Rafael I.} and Zhang, {Yao Zhong}",

note = "Funding Information: Financial support from the Australian Research Council (W.L.Y. and Y.Z.Z.) and the National Science Foundation under Grant PHY-0244261 (R.I.N.) is gratefully acknowledged.",

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T1 - Q-operator and T-Q relation from the fusion hierarchy

AU - Yang, Wen Li

AU - Nepomechie, Rafael I.

AU - Zhang, Yao Zhong

N1 - Funding Information: Financial support from the Australian Research Council (W.L.Y. and Y.Z.Z.) and the National Science Foundation under Grant PHY-0244261 (R.I.N.) is gratefully acknowledged.

PY - 2006/2/16

Y1 - 2006/2/16

N2 - We propose that the Baxter Q-operator for the spin-1/2 XXZ quantum spin chain is given by the j→∞ limit of the transfer matrix with spin-j (i.e., (2j+1)-dimensional) auxiliary space. Applying this observation to the open chain with general (non-diagonal) integrable boundary terms, we obtain from the fusion hierarchy the T-Q relation for generic values (i.e., not roots of unity) of the bulk anisotropy parameter. We use this relation to determine the Bethe ansatz solution of the eigenvalues of the fundamental transfer matrix. This approach is complementary to the one used recently to solve the same model for the roots of unity case.

AB - We propose that the Baxter Q-operator for the spin-1/2 XXZ quantum spin chain is given by the j→∞ limit of the transfer matrix with spin-j (i.e., (2j+1)-dimensional) auxiliary space. Applying this observation to the open chain with general (non-diagonal) integrable boundary terms, we obtain from the fusion hierarchy the T-Q relation for generic values (i.e., not roots of unity) of the bulk anisotropy parameter. We use this relation to determine the Bethe ansatz solution of the eigenvalues of the fundamental transfer matrix. This approach is complementary to the one used recently to solve the same model for the roots of unity case.

KW - Bethe ansatz

KW - Fusion hierarchy

KW - Q-operator

KW - Reflection equation

KW - Spin chain

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