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arXiv:hep-th/9707098 · Journal of Physics A Mathematical and General

Excited states in the twistedXXZspin chain

T Nassar, O Tirkkonen

Published Dec 11, 1998• 7 citations
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Abstract

We compute the finite-size spectrum for the spin- chain with twisted boundary conditions, for anisotropy in the regime , and arbitrary twist . The string hypothesis is employed for treating complex excitations. The Bethe ansatz equtions are solved within a coupled nonlinear integral equation approach, with one equation for each type of string. The root-of-unity quantum group invariant periodic chain reduces to the chain with a set of twist boundary conditions ( , an integer multiple of ). For this model, the restricted Hilbert space corresponds to a unitary conformal field theory, and we recover all primary states in the Kac table in terms of states with specific twist and strings.

DOI
10.1088/0305-4470/31/49/016

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In integrable spin chains, the spectral problem can be solved by the method of Bethe Ansatz, which transforms the problem of diagonalization of the Hamiltonian into the problem of solving a set of algebraic equations named Bethe equations. In this work, we systematically investigate the spin- s s XXX chain with twisted and open boundary conditions using the rational Q Q -system, which is a powerful tool to solve Bethe equations. We establish basic frameworks of the rational Q Q -system and confirm its completeness numerically in both cases. For twisted boundaries, we investigate the polynomiality conditions of the rational Q Q -system and derive physical conditions for singular solutions of Bethe equations. For open boundaries, we uncover novel phenomena such as hidden symmetries and boundary induced strings under specific boundary parameters. Hidden symmetries lead to the appearance of extra degeneracies in the Hilbert space, while the boundary induced string is a novel type of exact string configuration, whose length depends on the boundary magnetic fields. These findings, supported by both analytical and numerical evidences, offer new insights into the interplay between symmetries and boundary conditions.