Abstract
We study models of itinerant spinless fermions with random long-range interactions. We motivate such models from descriptions of fermionic atoms in multi-mode optical cavities. The solution of an infinite-range model yields a metallic phase which has glassy charge dynamics, and a localized glass phase with suppressed density of states at low energies. We compare these phases to the conventional disordered Fermi liquid, and the insulating electron glass of semiconductors. Prospects for the realization of such glassy phases in cold atom systems are discussed.
Highlights
There is much current interest in experiments with ultracold atoms and photons that provide clean realizations of models from condensed matter physics
The hope is that these quantum optics experiments eventually reach the parameter regimes and accuracy necessary to allow for predictions that can overcome the limitations of conventional theoretical approaches for strongly interacting quantum many-body systems
II, starting from a Jaynes-Cummings type Hamiltonian for itinerant fermions coupled to cavity photons, we derive the fermionic model that we study in this paper: H =−t i, j c†i c j + h.c
Summary
There is much current interest in experiments with ultracold atoms and photons that provide clean realizations of models from condensed matter physics. In a series of remarkable experiments at ETH Zurich [2,3,4], Baumann et al, have begun the quantum-simulation of strongly-interacting quantum gases with genuine long-range interactions [5] In these many-body cavity QED systems, an atomic ensemble (a thermal cloud [6, 7] or Bose-Einstein condensate) is loaded into an optical cavity containing quantized photon modes. An important hallmark of such insulating electron glasses is the Efros-Shklovskii gap in the single particle density of states in the glassy phase, whose elementary charge excitations are strongly Anderson localized Such a pseudogap is required by the stability of metastable states in the presence of unscreened long range interactions [28]. In the context of Coulomb frustrated systems in condensed matter (without disorder), an intermediate metallic phase with periodic, striped density order (”conducting crystal”) was discussed by Spivak and Kivelson [37]
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