Ym. Gufan et al., Geometric invariant theory approach to the determination of ground states of D-wave condensates in isotropic space, J MATH PHYS, 42(4), 2001, pp. 1533-1562
A complete and rigorous determination of the possible ground states for D-w
ave pairing Bose condensates is presented, using a geometrical invariant th
eory approach to the problem. The order parameter is argued to be a vector,
transforming according to a ten-dimensional real representation of the gro
up G = O(3)xU(1) x [T]. We determine the equalities and inequalities defini
ng 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 sys
tem. We find 15 allowed phases (besides the unbroken one), with different s
ymmetries, that we thoroughly determine. The group-subgroup relations betwe
en bordering phases are pointed out. The perturbative sixth degree correcti
ons to the minimum of a fourth degree polynomial G-invariant free energy, c
alculated by Mermin, are also determined. (C) 2001 American Institute of Ph
ysics.