A Class of Parameter Dependent Commuting Matrices

Details A Class of Parameter Dependent Commuting Matrices A Class of Parameter Dependent Commuting Matrices

2005-01-20

arxiv.org/abs/cond-mat/0501502v2

J. Phys. A38, L431 (2005).

Physics

Condensed Matter

Strongly Correlated Electrons

Latex, Added References, Typos corrected

Scientific paper

10.1088/0305-4470/38/23/L03

We present a novel class of real symmetric matrices in arbitrary dimension $d$, linearly dependent on a parameter $x$. The matrix elements satisfy a set of nontrivial constraints that arise from asking for commutation of pairs of such matrices for all $x$, and an intuitive sufficiency condition for the solvability of certain linear equations that arise therefrom. This class of matrices generically violate the Wigner von Neumann non crossing rule, and is argued to be intimately connected with finite dimensional Hamiltonians of quantum integrable systems.

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