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arXiv:cond-mat/0209265 · CRC Press eBooks

Integrability and exact solution of an electronic model with long range interactions

Katrina Hibberd, Jon Links

Published Nov 30, 2003• 1 citation
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Abstract

We present an electronic model with long range interactions. Through the quantum inverse scattering method, integrability of the model is established using a one- parameter family of typical irreducible representations of gl (2|l). The eigenvalues of the conserved operators are derived in terms of the Bethe ansatz, from which the energy eigenvalues of the Hamiltonian are obtained.

DOI
10.1201/9781482269079-146

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We present an electronic model with long range interactions. Through the quantum inverse scattering method, integrability of the model is established using a one- parameter family of typical irreducible representations of gl (2|l). The eigenvalues of the conserved operators are derived in terms of the Bethe ansatz, from which the energy eigenvalues of the Hamiltonian are obtained.
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Quantum integrability is established for the one-dimensional supersymmetric UUU model with boundary terms by means of the quantum inverse-scattering method. The boundary supersymmetric UUU chain is solved by using the coordinate-space Bethe-ansatz technique and Bethe-ansatz equations are derived. This provides us with a basis for computing the finite-size corrections to the low-lying energies in the system.
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An exactly solvable strongly correlated electron model with two independent parameters is constructed in the frame of the quantum inverse scattering method, which can be seen as a generalization of the Bariev model. Through the Bethe ansatz method, a set of Bethe ansatz equations is derived. In the thermodynamic limit, to study the ground state of the model, we obtain the integral equations for the density of Bethe roots. Numerical validation is done to confirm the accuracy of our analytic results.