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:Journal of mathematical physics 2001-04, Vol.42 (4), p.1533-1562
Main Authors: Gufan, Yu. M., Popov, Al. V., Sartori, G., Talamini, V., Valente, G., Vinberg, E. B.
Format: Article
Language:English
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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= O 3 ⊗ U 1 ×〈 T  〉. 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:0022-2488
1089-7658
DOI:10.1063/1.1345871