New Class of Solvable and Integrable Many-Body Models

R. W. Richardson

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arXiv · cond-mat/0203512

New Class of Solvable and Integrable Many-Body Models

R. W. Richardson

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Abstract

Integrability conditions for systems of bosons or fermions with seniority conserving hamiltonians are derived. The conditions are shown to be invariant under a large class of transformations of the interaction matrix elements. Previously published integrable models are shown to satisfy these conditions and the existence of a new class of integrable models is demonstrated. The number of free parameters in the interaction in these models equals the number of single particle levels plus 3 . Equations for the energy eigenstates and eigenvalues are derived and the eigenvalues of the complete set of two-body integrals of the motion are given for the new class. Some two-body correlations in these eigenstates are derived from the integrals of the motion.

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R. W. Richardson. 2002-03-26. New Class of Solvable and Integrable Many-Body Models. https://arxiv.org/abs/cond-mat/0203512

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