[en] We suggest a new mean-field method for studying the thermodynamic competition between magnetic and superconducting phases in a two-dimensional square lattice. A partition function is constructed by writing microscopic interactions that describe the exchange of density and spin fluctuations. A block structure dictated by spin, time-reversal, and bipartite symmetries is imposed on the single-particle Hamiltonian. The detailed dynamics of the interactions are neglected and replaced by a normal distribution of random matrix elements. The resulting partition function can be calculated exactly. The thermodynamic potential has a structure which depends only on the spectrum of quasiparticles propagating in fixed condensation fields, with coupling constants that can be related directly to the variances of the microscopic processes. The resulting phase diagram reveals a fixed number of phase topologies whose realizations depend on a single coupling parameter ratio, alpha. Most phase topologies are realized for a broad range of values of alpha and can thus be considered robust with respect to moderate variations in the detailed description of the underlying interactions.
Research center :
SUPRATECS - Services Universitaires pour la Recherche et les Applications Technologiques de Matériaux Électro-Céramiques, Composites, Supraconducteurs - ULiège
Disciplines :
Physics
Author, co-author :
Vanderheyden, Benoît ; Université de Liège - ULiège > Dép. d'électric., électron. et informat. (Inst.Montefiore) > Electronique et microsystèmes
Jackson, A. D.; The Niels Bohr International Academy, The Niels Bohr Institute, Copenhagen, Denmark
Language :
English
Title :
Random matrix model for antiferromagnetism and superconductivity on a two-dimensional lattice
Publication date :
2009
Journal title :
Physical Review. B, Condensed Matter and Materials Physics
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Expressed here in the momentum basis, the matrix Hμ of size N×N contains N2 /4 independent elements for Bμ and N2 /4+N/2 independent elements for Cμ, hence a total of N (N+1) /2 independent elements. This is also the number of independent elements found in the more familiar coordinate representation, where Hμ is real symmetric.
As is usually the case in random matrix theory, the technically convenient choice of a Gaussian distribution is completely passive. All final results will depend only on the inverse variances, Σb2, and identical results would be obtained for other choices of P (Hint) with equal variances.
