Boundary Energy of the Open XXZ Chain from New Exact Solutions

Murgan, Rajan; Nepomechie, Rafael I.; Shi, Chi

doi:10.1007/s00023-006-0286-4

Cited by 17 publications

(51 citation statements)

References 18 publications

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“…This result can be shown to coincide with previous results in [21,22]. We emphasize that the result (3.28) has been derived under the assumption that the Bethe roots for the ground state obey the string hypothesis, which is true only for suitable values of the boundary parameters.…”

Section: Jhep01(2007)038supporting

confidence: 89%

“…Thus, as in the even p case, there is no contribution to the boundary energy from extra roots. Proceeding as before, we find JHEP01(2007)038 that the energy contribution from each boundary is again given by (3.28), thus coinciding with previous results in [21,22]. As for even p, the derivation here is based on the string hypothesis for the ground-state Bethe roots, which is true only for suitable values of boundary parameters.…”

Section: Jhep01(2007)038supporting

confidence: 85%

“…The distribution of the real parts of these roots {ṽ k } can be represented by a density function, which is computed from the counting function. To this end, following [21,22] and references therein, we define some basic quantities …”

Section: Jhep01(2007)038mentioning

confidence: 99%

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Boundary energy of the general open XXZ chain at roots of unity

Murgan

Nepomechie

Shi

2007

J. High Energy Phys.

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Section: Jhep01(2007)038supporting

confidence: 89%

Section: Jhep01(2007)038supporting

confidence: 85%

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Boundary energy of the general open XXZ chain at roots of unity

Murgan

Nepomechie

Shi

2007

J. High Energy Phys.

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“…In Sect. 2, we review our Bethe ansatz solutions for special case at roots of unity [8] which we utilize to compute the boundary (surface) energy of the XXZ chain [9]. Next, in Sect.…”

Section: Introductionmentioning

confidence: 99%

Bethe ansatz and boundary energy of the open spin-1/2 XXZ chain

Murgan

2006

Czech J Phys

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We review recent results on the Bethe ansatz solutions for the eigenvalues of the transfer matrix of an integrable open XXZ quantum spin chain using functional relations which the transfer matrix obeys at roots of unity. First, we consider a case where at most two of the boundary parameters c~_, c~+, /3_, t3+ are nonzero. A generalization of the Baxter T-Q equation that involves more than one independent Q is described. We use this solution to compute the boundary energy of the chain in the thermodynamic limit. We conclude the paper with a review of some results for the general integrable boundary terms, where all six boundary parameters are arbitrary.

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“…More recently, a Bethe-type solution has also been obtained for arbitrary (generic) boundary parameters provided the anisotropy parameter takes special values (q is a root of unity) [9]. However, for generic integrable boundary conditions and anisotropy parameter the exact spectrum of (1) has remained an outstanding problem.…”

Section: Introductionmentioning

confidence: 99%

Exact spectrum of the XXZ open spin chain from theq-Onsager algebra representation theory

2007

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The transfer matrix of the XXZ open spin-1 2 chain with general integrable boundary conditions and generic anisotropy parameter (q is not a root of unity and |q| = 1) is diagonalized using the representation theory of the q−Onsager algebra. Similarly to the Ising and superintegrable chiral Potts models, the complete spectrum is expressed in terms of the roots of a characteristic polynomial of degree d = 2 N . The complete family of eigenstates are derived in terms of rational functions defined on a discrete support which satisfy a system of coupled recurrence relations. In the special case of linear relations between left and right boundary parameters for which Bethe-type solutions are known to exist, our analysis provides an alternative derivation of the results of Nepomechie et al. and Cao et al.. In the latter case the complete family of eigenvalues and eigenstates splits in two sets, each associated with a characteristic polynomial of degree d < 2 N . Numerical checks performed for small values of N support the analysis.

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Boundary Energy of the Open XXZ Chain from New Exact Solutions

Cited by 17 publications

References 18 publications

Boundary energy of the general open XXZ chain at roots of unity

Boundary energy of the general open XXZ chain at roots of unity

Bethe ansatz and boundary energy of the open spin-1/2 XXZ chain

Exact spectrum of the XXZ open spin chain from theq-Onsager algebra representation theory

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