M. V. Feigel’man 1, 2, L. B. Ioffe 1, 3, 4, M. Mézard 3
Physical Review B 82 (2010) 184534
We develop an analytical theory for generic disorder-driven quantum phase transitions. We apply this formalism to the superconductor-insulator transition and we briefly discuss the applications to the order-disorder transition in quantum magnets. The effective spin-1/2 models for these transitions are solved in the cavity approximation which becomes exact on a Bethe lattice with large branching number K >> 1 and weak dimensionless coupling g << 1. The characteristic features of the low temperature phase is a large self-formed inhomogeneity of the order-parameter distribution near the critical point K_{c}(g) where the critical temperature T_{c} of the ordering transition vanishes. Near the quantum critical point, the typical value of the order parameter vanishes exponentially, B_{0}\propto e^{-C/(K-K_{c}(g))}. In the disordered regime, realized at K
- 1. L.D. Landau Institute for Theoretical Physics,
Landau Institute for Theoretical Physics - 2. Moscow Institute of Physics and Technology (MIPT),
Moscow Institute of Physics and Technology - 3. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
CNRS : UMR8626 – Université Paris XI – Paris Sud - 4. Department of Physics and Astronomy,
University of California, Riverside