Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userRenormalization group study of quantum criticality in gapped Kondo model
101
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
Quantum impurity models are the prototypical examples of quantum many-body dynamics which manifests in their spectral and transport properties. Single channel Anderson(and Kondo model) leads to the Fermi liquid ground state in the strong coupling regime which corresponds to a stable infrared fixed point at which the quantum impurity gets completely screened by the conduction electrons. Quantum impurity models with non-trivial density of states exhibit quantum phase transition and this quantum criticality lies in the universality class of local quantum critical systems. In this paper, we report first study of the flow equation renormalization of gapped Kondo model which has gapped density of states, the gap being at the Fermi level. Flow equation renormalization group method has proved to be one of the very robust renormalization methods to study Kondo physics both in equilibrium as well as in non-equilibrium. Here we have shown that this method can also be employed to study local quantum criticality. We have calculated the flow equations for the Kondo coupling and solved them for various values of the gap parameter and we find that there is suppression of Kondo divergence as gap is increased which signifies that as gap is increased, renormalization flow goes away from the strong coupling fixed point. We have also calculated the spin susceptibility and we find that as gap is increased, susceptibility goes over to the Curie behaviour and hence confirming the renormalization flow towards the local moment fixed point.
rate research
Read More
The tunneling conductance is calculated as a function of the gate voltage in wide temperature range for the single quantum dot systems with Coulomb interaction. We assume that two orbitals are active for the tunneling process. We show that the Kondo temperature for each orbital channel can be largely different. The tunneling through the Kondo resonance almost fully develops in the region $T lsim 0.1 T_{K}^{*} sim 0.2 T_{K}^{*}$, where $T_{K}^{*}$ is the lowest Kondo temperature when the gate voltage is varied. At high temperatures the conductance changes to the usual Coulomb oscillations type. In the intermediate temperature region, the degree of the coherency of each orbital channel is different, so strange behaviors of the conductance can appear. For example, the conductance once increases and then decreases with temperature decreasing when it is suppressed at T=0 by the interference cancellation between different channels. The interaction effects in the quantum dot systems lead the sensitivities of the conductance to the temperature and to the gate voltage.
Thermodynamic properties are presented for four magnetic impurity models describing delocalized fermions scattering from a localized orbital at an energy-dependent rate $Gamma(epsilon)$ which vanishes precisely at the Fermi level, $epsilon = 0$. Specifically, it is assumed that for small $|epsilon|$, $Gamma(epsilon)propto|epsilon|^r$ with $r>0$. The cases $r=1$ and $r=2$ describe dilute magnetic impurities in unconventional superconductors, ``flux phases of the two-dimensional electron gas, and zero-gap semiconductors. For the nondegenerate Anderson model, the depression of the low-energy scattering rate suppresses mixed valence in favor of local-moment behavior, and leads to a marked reduction in the exchange coupling on entry to the local-moment regime, with a consequent narrowing of the range of parameters within which the impurity spin becomes Kondo-screened. The relationship between the Anderson model and the exactly screened Kondo model with power-law exchange is examined. The intermediate-coupling fixed point identified in the latter model by Withoff and Fradkin (WF) has clear signatures in the thermodynamic properties and in the local magnetic response of the impurity. The underscreened, impurity-spin-one Kondo model and the overscreened, two-channel Kondo model both exhibit a conditionally stable intermediate-coupling fixed point in addition to unstable fixed points of the WF type. In all four models, the presence or absence of particle-hole symmetry plays a crucial role.
We theoretically investigate the non-equilibrium quantum phase transition in a generic setup: the pseudogap Kondo model where a quantum dot couples to two-left (L) and right (R)-voltage-biased fermionic leads with power-law density of states (DOS) with respect to their Fermi levels {mu}_L/R, {rho}_c,L(R) ({omega}) propto |{omega} - {mu}_L(R) |r, and 0 < r < 1. In equilibrium (zero bias voltage) and for 0 < r < 1/2, with increasing Kondo correlations, in the presence of particle-hole symmetry this model exhibits a quantum phase transition from a unscreened local moment (LM) phase to the Kondo phase. Via a controlled frequency-dependent renormalization group (RG) approach, we compute analytically and numerically the non-equilibrium conductance, conduction electron T-matrix and local spin susceptibility at finite bias voltages near criticality. The current-induced decoherence shows distinct nonequilibrium scaling, leading to new universal non-equilibrium quantum critical behaviors in the above observables. Relevance of our results for the experiments is discussed.
Critical transition points between symmetry-broken phases are characterized as fixed points in the renormalization group (RG) theory. We show that, following the standard Wilsonian procedure that traces out the large momentum modes, this well known fact can break down in non-Hermitian systems. Based on non-Hermitian Su-Schrieffer-Hegger (SSH)-type models, we propose a real-space decimation scheme to study the criticality between the topological and trivial phase. We provide concrete examples and an analytic proof to show that the real-space scheme perfectly overcomes the insufficiency of the standard method, especially in the sense that it always preserves the system at criticality as fixed points under RG. The proposed method can also greatly simplify the search of critical points for complicated non-Hermitian models by ruling out the irrelevant operators. These results pave the way towards more advanced RG-based techniques for the interacting non-Hermitian quantum systems.
We examine the exchange Hamiltonian for magnetic adatoms in graphene with localized inner shell states. On symmetry grounds, we predict the existence of a class of orbitals that lead to a distinct class of quantum critical points in graphene, where the Kondo temperature scales as $T_{K}propto|J-J_{c}|^{1/3}$ near the critical coupling $J_{c}$, and the local spin is effectively screened by a emph{super-ohmic} bath. For this class, the RKKY interaction decays spatially with a fast power law $sim1/R^{7}$. Away from half filling, we show that the exchange coupling in graphene can be controlled across the quantum critical region by gating. We propose that the vicinity of the Kondo quantum critical point can be directly accessed with scanning tunneling probes and gating.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
