Universal quantum glass transition on the Bethe lattice

We study the Coulomb glass behavior emerging from the interplay of interactions and disorder, by examining a model of spinless fermions at half filling on the Bethe lattice [1,2]. We consider the limit of infinite coordination number, where we combine dynamical mean field theory with a Hartree-Fock approximation to investigate the glass transition and the properties of the glassy phase in the presence of full replica symmetry breaking. This approach allows us to study the opening of the Efros-Shklovskii pseudogap in the glassy phase, and grants us access to the spectral function. In particular, we demonstrate the universal scaling collapse of the pseudogap and the spectral function at close to zero temperatures, where the melting of the glass is governed by the quantum fluctuations induced by the hopping of fermions. We show that this quantum scaling function differs from the classical scaling function of the thermal transition of the spin glass limit. Our results should be relevant for the glassy dynamics observed in Si inversion layers, persisting in the metallic phase [3].

[1] A. A. Pastor and V. Dobrosavljevic, Phys. Rev. Lett. 83, 4642 (1999).
[2] M. Mueller and S. Pankov, Phys. Rev. B 75, 144201 (2007).
[3] S. Bogdanovich and D. Popovic, Phys. Rev. Lett. 88, 236401 (2002).