Journal
PHYSICAL REVIEW B
Volume 82, Issue 18, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevB.82.184534
Keywords
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Funding
- Triangle de la physique 2007-36 [ANR-06-BLAN-0218, ECS-0608842]
- ARO [56446-PH-QC]
- DARPA [HR0011-09-1-0009]
- Russian Academy of Sciences
- RFBR [10-02-00554]
- Agence Nationale de la Recherche (ANR) [ANR-06-BLAN-0218] Funding Source: Agence Nationale de la Recherche (ANR)
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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 feature of the low-temperature phase is a large self-formed inhomogeneity of the order-parameter distribution near the critical point K >= K-c(g), where the critical temperature T-c of the ordering transition vanishes. We find that the local probability distribution P(B) of the order parameter B has a long power-law tail in the region where B is much larger than its typical value B-0. Near the quantum-critical point, at K -> K-c(g), the typical value of the order parameter vanishes exponentially, B-0 proportional to e(-C/[K-Kc(g)]) while the spatial scale N-inh of the order parameter inhomogeneities diverges as [K-K-c(g)](-2). In the disordered regime, realized at K
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