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arXiv:hep-th/9607012

Completeness of Bethe's states for generalized $XXZ$ model, II

Anatol N. Kirillov, Nadejda A. Liskova

Published Jul 2, 1996• 1 citation
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Abstract

For any rational number $p_0\ge 2$ we prove an identity of Rogers-Ramanujan's type. Bijection between the space od states for $XXZ$ model and that of $XXX$ model is constructed

DOI
10.48550/arxiv.hep-th/9607012

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Completeness of Bethe's states for generalized XXZXXZXXZ model, II
For any rational number p0≥2p_0\ge 2p0​≥2 we prove an identity of Rogers-Ramanujan's type. Bijection between the space od states for XXZXXZXXZ model and that of XXXXXXXXX model is constructed
For any rational number p0≥1p_0\ge 1p0​≥1 we prove an identity of Rogers-Ramanujan-Gordon-Andrews' type. Bijection between the space of states for XXZ model and that of XXX model is constructed.
The finite-volume spectrum of an integrable massive perturbation of a rational conformal field theory interpolates between massive multiparticle states in infinite-volume (IR limit) and conformal states, which are approached at zero volume (UV limit). Each state is labeled in the IR by a set of “Bethe-ansatz quantum numbers,” while in the UV limit it is characterized primarily by the conformal dimensions of the conformal field creating it. We present explicit conjectures for the UV conformal dimensions corresponding to any IR state in the ϕ1, 3-perturbed minimal models ℳ(2, 5) and ℳ(3, 5). The conjectures, which are based on a combinatorial interpretation of the Rogers-Ramanujan-Schur identities, are consistent with numerical results obtained previously for low-lying energy levels.
Completeness of Wronskian Bethe Equations for Rational glm∣n{\mathfrak {\mathfrak {gl}}_{{{\mathsf {m}}}|{{\mathsf {n}}}}}glm∣n​ Spin Chains