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arXiv:1208.1988 · Nature

Quantum phase transition in a resonant level coupled to interacting leads

Henok T. Mebrahtu, Ivan Valerievich Borzenets, Dong E. Liu, Huaixiu Zheng, Yuriy Bomze, Alex I. Smirnov, Harold U. Baranger, Gleb Finkelstein

Published Jul 31, 2012• 92 citations
arXivHTMLPDF
DOI
10.1038/nature11265

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We study tunneling through a resonant level connected to two dissipative bosonic baths: one is the resistive environment of the source and drain leads, while the second comes from coupling to potential fluctuations on a resistive gate. We show that several quantum phase transitions (QPT) occur in such a model, transitions which emulate those found in interacting systems such as Luttinger liquids or Kondo systems. We first use bosonization to map this dissipative resonant level model to a resonant level in a Luttinger liquid, one with, curiously, two interaction parameters. Drawing on methods for analyzing Luttinger liquids at both weak and strong coupling, we obtain the phase diagram. For strong dissipation, a Berezinsky-Kosterlitz-Thouless QPT separates strong-coupling and weak-coupling (charge localized) phases. In the source-drain symmetric case, all relevant backscattering processes disappear at strong coupling, leading to perfect transmission at zero temperature. In fact, a QPT occurs as a function of the coupling asymmetry or energy of the resonant level: the two phases are (i) the system is cut into two disconnected pieces (zero transmission), or (ii) the system is a single connected piece with perfect transmission, except for a disconnected fractional degree of freedom. The latter arises from the competition between the two fermionic leads (source and drain), as in the two-channel Kondo effect.
The dipole-coupled two-level atoms (qubits) in a single-mode resonant cavity are studied by extended bosonic coherent states. The numerical solution is presented. The first-order quantum phase transitions may occur in finite systems, in contrast to the original Dicke model. This system also exhibits a second-order quantum phase transition from the normal to the superradiant phase, as in the original Dicke model. Finite-size scaling for several observables---such as average fidelity susceptibility, order parameter, and concurrence---is performed for different interatomic interactions. The scaling exponents obtained suggest that interatomic interactions do not change the universality class.
We consider two-species of fermions in a rotating trap that interact via an s-wave Feshbach resonance, at total Landau level filling factor two (or one for each species). We show that the system undergoes a quantum phase transition from a fermion integer quantum Hall state to a boson fractional quantum Hall state as the pairing interaction strength increases, with the transition occurring near the resonance. The effective field theory for the transition is shown to be that of a (emergent) massless relativistic bosonic field coupled to a Chern-Simons gauge field, with the coupling giving rise to semionic statistics to the emergent particles.