Separation of variables for integrable spin–boson models
We formulate the functional Bethe ansatz for bosonic (infinite dimensional) representations of the Yang–Baxter algebra. The main deviation from the standard approach consists in a half infinite Sklyanin lattice made of the eigenvalues of the operator zeros of the Bethe annihilation operator. By a se...
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Published in | Nuclear physics. B Vol. 839; no. 3; pp. 604 - 626 |
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Main Authors | , , , |
Format | Journal Article |
Language | English |
Published |
Elsevier B.V
01.11.2010
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Subjects | |
Online Access | Get full text |
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Summary: | We formulate the functional Bethe ansatz for bosonic (infinite dimensional) representations of the Yang–Baxter algebra. The main deviation from the standard approach consists in a half infinite
Sklyanin lattice made of the eigenvalues of the operator zeros of the Bethe annihilation operator. By a separation of variables, functional
TQ-equations are obtained for this half infinite lattice. They provide valuable information about the spectrum of a given Hamiltonian model. We apply this procedure to integrable spin–boson models subject to both twisted and open boundary conditions. In the case of general twisted and certain open boundary conditions polynomial solutions to these
TQ-equations are found and we compute the spectrum of both the full transfer matrix and its quasi-classical limit. For generic open boundaries we present a two-parameter family of Bethe equations, derived from
TQ-equations that are compatible with polynomial solutions for Q. A connection of these parameters to the boundary fields is still missing. |
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ISSN: | 0550-3213 1873-1562 |
DOI: | 10.1016/j.nuclphysb.2010.07.005 |