Searching for degeneracies of real Hamiltonians using homotopy classification of loops in SO(n)
2005 (English)In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 71, no 1, 012106- p.Article in journal (Refereed) Published
Topological tests to detect degeneracies of Hamiltonians have been put forward in the past. Here, we address the applicability of a recently proposed test [Phys. Rev. Lett. 92, 060406 (2004)] for degeneracies of real Hamiltonian matrices. This test relies on the existence of nontrivial loops in the space of eigenbases SO$(n)$. We develop necessary means to determine the homotopy class of a given loop in this space. Furthermore, in cases where the dimension of the relevant Hilbert space is large the application of the original test may not be immediate. To remedy this deficiency, we put forward a condition for when the test is applicable to a subspace of Hilbert space. Finally, we demonstrate that applying the methodology of [Phys. Rev. Lett. 92, 060406 (2004)] to the complex Hamiltonian case does not provide any new information.
Place, publisher, year, edition, pages
2005. Vol. 71, no 1, 012106- p.
SO(n), topological tests of degeneracies
Physical Sciences Atom and Molecular Physics and Optics
Research subject Physics with specialization in Quantum Chemistry; Physics and Astronomy specializing in Theoretical Physics
IdentifiersURN: urn:nbn:se:uu:diva-75526DOI: 10.1103/PhysRevA.71.012106ISI: 000227283300022OAI: oai:DiVA.org:uu-75526DiVA: diva2:103437