We study a mixture of ultracold spin-half fermionic and spin-one bosonic atoms in a shallow optical lattice where the bosons are coupled to the fermions via both density-density and spin-spin interactions. We consider the parameter regime where the b
osons are in a superfluid ground state, integrate them out, and obtain an effective action for the fermions. We carry out a renormalization group analysis of this effective fermionic action at low temperatures, show that the presence of the spinor bosons may lead to a separation of Fermi surfaces of the spin-up and spin-down fermions, and investigate the parameter range where this phenomenon occurs. We also calculate the susceptibilities corresponding to the possible superfluid instabilities of the fermions and obtain their possible broken-symmetry ground states at low temperatures and weak interactions.
For the one-dimensional Holstein model, we show that the relations among the scaling exponents of various correlation functions of the Tomonaga Luttinger liquid (LL), while valid in the thermodynamic limit, are significantly modified by finite size c
orrections. We obtain analytical expressions for these corrections and find that they decrease very slowly with increasing system size. The interpretation of numerical data on finite size lattices in terms of LL theory must therefore take these corrections into account. As an important example, we re-examine the proposed metallic phase of the zero-temperature, half-filled one-dimensional Holstein model without employing the LL relations. In particular, using quantum Monte Carlo calculations, we study the competition between the singlet pairing and charge ordering. Our results do not support the existence of a dominant singlet pairing state.
In this paper, we describe the formation of local resonances in graphene in the presence of magnetic adatoms containing localized orbitals of arbitrary symmetry, corresponding to any given angular momentum state. We show that quantum interference eff
ects which are naturally inbuilt in the honeycomb lattice in combination with the specific orbital symmetry of the localized state lead to the formation of fingerprints in differential conductance curves. In the presence of Jahn-Teller distortion effects, which lift the orbital degeneracy of the adatoms, the orbital symmetries can lead to distinctive signatures in the local density of states. We show that those effects allow scanning tunneling probes to characterize adatoms and defects in graphene.
We examine theoretically the signatures of magnetic adatoms in graphene probed by scanning tunneling spectroscopy (STS). When the adatom hybridizes equally with the two graphene sublattices, the broadening of the local adatom level is anomalous and c
an scale with the cube of the energy. In contrast to ordinary metal surfaces, the adatom local moment can be suppressed by the proximity of the probing scanning tip. We propose that the dependence of the tunneling conductance on the distance between the tip and the adatom can provide a clear signature for the presence of local magnetic moments. We also show that tunneling conductance can distinguish whether the adatom is located on top of a carbon atom or in the center of a honeycomb hexagon.
