Geometric invariant theory approach to the determination of ground states of D-wave condensates in isotropic space

A complete and rigorous determination of the possible ground states for D-wave pairing Bose condensates is presented, using a geometrical invariant theory approach to the problem. The order parameter is argued to be a vector, transforming according to a ten dimensional real representation of the gro...

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Bibliographic Details
Published in:arXiv.org 2001-03
Main Authors: Gufan, Yu M, Popov, Al V, Sartori, G, Talamini, V, Valente, G, Vinberg, E B
Format: Article
Language:English
Subjects:
Condensates
Free energy
Ground state
Invariants
Mathematical analysis
Order parameters
Phases
Polynomials
Subgroups
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Summary:A complete and rigorous determination of the possible ground states for D-wave pairing Bose condensates is presented, using a geometrical invariant theory approach to the problem. The order parameter is argued to be a vector, transforming according to a ten dimensional real representation of the group \(G=\){\bf O}\(_3\otimes\){\bf U}\(_1\times \). We determine the equalities and inequalities defining the orbit space of this linear group and its symmetry strata, which are in a one-to-one correspondence with the possible distinct phases of the system. We find 15 allowed phases (besides the unbroken one), with different symmetries, that we thoroughly determine. The group-subgroup relations between bordering phases are pointed out. The perturbative sixth degree corrections to the minimum of a fourth degree polynomial \(G\)-invariant free energy, calculated by Mermin, are also determined.
ISSN:2331-8422
DOI:10.48550/arxiv.0009080