Quantum relativistic Toda chain at root of unity: isospectrality, modified Q-operator, and functional Bethe ansatz
We investigate an N-state spin model called quantum relativistic Toda chain and based on the unitary finite-dimensional representations of the Weyl algebra with q being Nth primitive root of unity. Parameters of the finite-dimensional representation of the local Weyl algebra form the classical dis...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2002-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171202105059 |
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| Summary: | We investigate an N-state spin model called quantum
relativistic Toda chain and based on the unitary
finite-dimensional representations of the Weyl algebra with q
being Nth primitive root of unity. Parameters of the
finite-dimensional representation of the local Weyl algebra form
the classical discrete integrable system. Nontrivial dynamics of
the classical counterpart corresponds to isospectral
transformations of the spin system. Similarity operators are
constructed with the help of modified Baxter's Q-operators. The
classical counterpart of the modified Q-operator for the initial
homogeneous spin chain is a Bäcklund transformation.
This transformation creates an extra Hirota-type soliton in a
parameterization of the chain structure. Special choice of values
of solitonic amplitudes yields a degeneration of spin
eigenstates, leading to the quantum separation of variables, or
the functional Bethe ansatz. A projector to the separated
eigenstates is constructed explicitly as a product of modified
Q-operators. |
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| ISSN: | 0161-1712 1687-0425 |