Quantum renormalization group and excitonic phase transition in a strong magnetic field

The critical behavior of excitonic fluctuations is investigated at low temperatures. The Wilson renormalization group is applied to a generalized free-energy functional of the Landau-Ginzburg-Wilson type, which is derived by coarse-graining a microscopic functional. The quantum mechanical effects give rise to an increase of the effective dimensionality at zero temperature. The values of this increase z are z = 1 for a semiconductor and z = 2 for a semimetal, depending on whether the electronic density of states is zero at the Fermi energy or not, respectively. Quantum-classical crossover phenomena appear at a finite but low temperature. As the phase transition point is approached in a semimetal the critical fluctuations in real space first grow two-dimensionally in the plane perpendicular to the magnetic field and then develop three-dimensionally. It is explicitly shown that the mean field theory breaks down in a semiconductor.Correspondence and reprint requests should be addressed to Tatsuzo Nagai.