Document Type
Article
Date of Original Version
8-2000
Abstract
For a two-spin model which is (classically) integrable on a five-dimensional hypersurface in six-dimensional parameter space and for which level degeneracies occur exclusively (with one known exception) on four-dimensional manifolds embedded in the integrability hypersurface, we investigate the relations between symmetry, integrability, and the assignment of quantum numbers to eigenstates. We calculate quantum invariants in the form of expectation values for selected operators and monitor their dependence on the Hamiltonian parameters along loops within, without, and across the integrability hypersurface in parameter space. We find clear-cut signatures of integrability and nonintegrability in the observed traces of quantum invariants evaluated in finite-dimensional invariant Hilbert subspaces. The results support the notion that quantum integrability depends on the existence of action operators as constituent elements of the Hamiltonian.
Citation/Publisher Attribution
Stepanov, V. V., & Müller, G. (2000). Signatures of quantum integrability and nonintegrability in the spectral properties of finite Hamiltonian matrices. Physical Review E, 62(2), 2008-2017. doi: 10.1103/PhysRevE.62.2008
Available at: http://dx.doi.org/10.1103/PhysRevE.62.2008
Terms of Use
All rights reserved under copyright.
Publisher Statement
© 2000 The American Physical Society