Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2010-09-21
Phys.Rev.D82:125027,2010
Physics
High Energy Physics
High Energy Physics - Theory
10 pages, 6 figures; v2: corrected typos and references, version accepted for publication in PRD
Scientific paper
10.1103/PhysRevD.82.125027
In this work we present two correspondences between the massless Gross-Neveu model with one or two coupling constants in 1+1 dimensions and nonrelativistic field theories in 3+1 dimensions. It is shown that on a mean-field level the massless Gross-Neveu model can be mapped onto BCS theory provided that translational invariance of the condensate is assumed. The generalized massless Gross-Neveu model with two coupling constants is mapped onto a quasi one-dimensional extended Hubbard model used in the description of spin-Peierls systems. It is shown that the particle hole symmetry of the Hubbard model implies self-consistency of the condensate. The dimensional reduction allows an identification of the phase diagrams of the models.
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