We develop a renormalization group approach for analyzing Frohlich polarons and apply it to a problem of impurity atoms immersed in a Bose-Einstein condensate of ultra cold atoms. Polaron energies obtained by our method are in excellent agreement with recent diagrammatic Monte Carlo calculations for a wide range of interaction strengths. We calculate the effective mass of polarons and find a smooth crossover from weak to strong coupling regimes. Possible experimental tests of our results in current experiments with ultra cold atoms are discussed.
The phase transition to superfluidity and the BCS-BEC crossover for an ultracold gas of fermionic atoms is discussed within a functional renormalization group approach. Non-perturbative flow equations, based on an exact renormalization group equation
, describe the scale dependence of the flowing or average action. They interpolate continuously from the microphysics at atomic or molecular distance scales to the macroscopic physics at much larger length scales, as given by the interparticle distance, the correlation length, or the size of the experimental probe. We discuss the phase diagram as a function of the scattering length and the temperature and compute the gap, the correlation length and the scattering length for molecules. Close to the critical temperature, we find the expected universal behavior. Our approach allows for a description of the few-body physics (scattering and molecular binding) and the many-body physics within the same formalism.
We present a non-perturbative renormalization-group approach to the Bose-Hubbard model. By taking as initial condition of the RG flow the (local) limit of decoupled sites, we take into account both local and long-distance fluctuations in a nontrivial
way. This approach yields a phase diagram in very good quantitative agreement with the quantum Monte Carlo results and reproduces the two universality classes of the superfluid--Mott-insulator transition with a good estimate of the critical exponents. Furthermore, it reveals the crucial role of the Ginzburg length as a crossover length between a weakly- and a strongly-correlated superfluid phase.
The crossover between low and high density regimes of exciton-polariton condensates is examined using a BCS wavefunction approach. Our approach is an extension of the BEC-BCS crossover theory for excitons, but includes a cavity photon field. The appr
oach can describe both the low density limit, where the system can be described as a Bose-Einstein condensate (BEC) of exciton-polaritons, and the high density limit, where the system enters a photon dominated regime. In contrast to the exciton BEC-BCS crossover where the system approaches an electron-hole plasma, the polariton high density limit has strongly correlated electron-hole pairs. At intermediate densities, there is a regime with BCS-like properties, with a peak at non-zero momentum of the singlet pair function. We calculate the expected photoluminescence and give several experimental signatures of the crossover.
We show how the density-matrix numerical renormalization group (DM-NRG) method can be used in combination with non-Abelian symmetries such as SU(N), where the decomposition of the direct product of two irreducible representations requires the use of
a so-called outer multiplicity label. We apply this scheme to the SU(3) symmetrical Anderson model, for which we analyze the finite size spectrum, determine local fermionic, spin, superconducting, and trion spectral functions, and also compute the temperature dependence of the conductance. Our calculations reveal a rich Fermi liquid structure.
An impurity immersed in a Bose-Einstein condensate is no longer accurately described by the Frohlich Hamiltonian as the coupling between the impurity and the boson bath gets stronger. We study the dominant effects of the two-phonon terms beyond the F
rohlich model on the ground-state properties of the polaron using Feynmans variational path-integral approach. The previously reported discrepancy in the effective mass between the renormalization group approach and this theory is shown to be absent in the beyond-Frohlich model on the positive side of the Feshbach resonance. Self-trapping, characterized by a sharp and dramatic increase of the effective mass, is no longer observed for the repulsive polaron once the two-phonon interactions are included. For the attractive polaron we find a divergence of the ground-state energy and effective mass at weaker couplings than previously observed within the Frohlich model.
F. Grusdt
,Y. E. Shchadilova
,A. N. Rubtsov
.
(2014)
.
"Renormalization group approach to the Frohlich polaron model: application to impurity-BEC problem"
.
Fabian Grusdt
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