Classification of Parameter-Dependent Quantum Integrable Models, Their Parameterization, Exact Solution, and Other Properties

Haile K. Owusu; Emil A. Yuzbashyan

doi:10.1088/1751-8113/44/39/395302

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arXiv · 1106.1831

Classification of Parameter-Dependent Quantum Integrable Models, Their Parameterization, Exact Solution, and Other Properties

Haile K. Owusu·Emil A. Yuzbashyan

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Abstract

We study general quantum integrable Hamiltonians linear in a coupling constant and represented by finite NxN real symmetric matrices. The restriction on the coupling dependence leads to a natural notion of nontrivial integrals of motion and classification of integrable families into Types according to the number of such integrals. A Type M family in our definition is formed by N-M nontrivial mutually commuting operators linear in the coupling. Working from this definition alone, we parameterize Type M operators, i.e. resolve the commutation relations, and obtain an exact solution for their eigenvalues and eigenvectors. We show that our parameterization covers all Type 1, 2, and 3 integrable models and discuss the extent to which it is complete for other types. We also present robust numerical observation on the number of energy level crossings in Type M integrable systems and analyze the taxonomy of types in the 1d Hubbard model.

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Haile K. Owusu, Emil A. Yuzbashyan. 2011-06-09. Classification of Parameter-Dependent Quantum Integrable Models, Their Parameterization, Exact Solution, and Other Properties. https://doi.org/10.1088/1751-8113/44/39/395302

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