Julio Abad

Exact solution of an electron system combining two different t-J models

A new strongly correlated electron model is presented. This is formed by two types of sites: one where double occupancy is forbidden, as in the t-J model, and the other where double occupancy is allowed but vacancy is not allowed, as in an inverse t-J model. The Hamiltonian shows nearest and next-to-nearest neighbour interactions and it is solved by means of a modified algebraic nested Bethe ansatz. The number of sites where vacancy is not allowed, may be treated as a new parameter if the model is regarded as a t-J model with impurities. The ground and excited states are described in the thermodynamic limit.

Integrable su(3) spin chain combining different representations

The general expression for the local matrix of a quantum chain with the site space in any representation of su(3) is obtained. This is made by generalizing from the fundamental representation and imposing the fulfilment of the Yang - Baxter equation. Then, a non-homogeneous spin chain combining different representations of su(3) is solved by developing a method inspired in the nested Bethe ansatz. The solution for the eigenvalues of the trace of the monodromy matrix is given as two coupled Bethe equations. A conjecture about the solution of a chain with the site states in different representations of su(n) is presented. The thermodynamic limit of the ground state is calculated.

A new expansion of the confluent hypergeometric function in terms of modified Bessel functions

Abstract An asymptotic expansion of the confluent hypergeometric function U(a,b,x) for large positive 2a − b is given in terms of modified Bessel functions multiplied by Buchholz polynomials, a family of double polynomials in the variables b and x with rational coefficients.

Buchholz polynomials: a family of polynomials relating solutions of confluent hypergeometric and Bessel equations

Abstract The expansion given by H. Buchholz, that allows one to express the regular confluent hypergeometric function M(a,b,z) as a series of modified Bessel functions with polynomial coefficients, is generalized to any solution of the confluent hypergeometric equation, by using a differential recurrence obeyed by the Buchholz polynomials.

Excitations and the S-matrix for an su(3) spin chain combining and representations

The associated Hamiltonian for an su(3) spin chain combining and representations is calculated. The ansatz equations for this chain are obtained and solved in the thermodynamic limit, and the ground state and excitations are described. Thus, relations between the number of roots and the number of holes in each level have been found. The excited states are characterized by means of these quantum numbers. Finally, the exact S-matrix for a state with two holes is found.

Method for solving integrable A2 spin chains combining different representations.

A non homogeneous spin chain in the representations

An algorithm to obtain global solutions of the double confluent Heun equation

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Diagonal solutions to reflection equations in higher spin models

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Computation of the Regular Confluent Hypergeometric Function

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Two new asymptotic expansions of the ratio of two gamma functions

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