Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userEffective low-energy description of the two impurity Anderson model: RKKY interaction and quantum criticality
156
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We show that the RKKY interaction in the two-impurity Anderson model comprise two contributions: a ferromagnetic part stemming from the symmetrized hybridization functions and an anti-ferromagnetic part. We demonstrate that this anti-ferromagnetic contribution can also be generated by an effective local tunneling term between the two impurities. This tunneling can be analytically calculated for particle-hole symmetric impurities. Replacing the full hybridization functions by the symmetric part and this tunneling term leads to the identical low-temperature fixed point spectrum in the numerical renormalization group. Compensating this tunneling term is used to restore the Varma-Jones quantum critical point between a strong coupling phase and a local singlet phase even in the absence of particle-hole symmetry in the hybridization functions. We analytically investigate the spatial frequencies of the effective tunneling term based on the combination of the band dispersion and the shape of the Fermi surface. Numerical renormalization group calculations provide a comparison of the distance dependent tunneling term and the local spin-spin correlation function. Derivations between the spatial dependency of the full spin-spin correlation function and the textbook RKKY interaction are reported.
rate research
Read More
We investigate static and dynamical ground-state properties of the two-impurity Anderson model at half filling in the limit of vanishing impurity separation using the dynamical density-matrix renormalization group method. In the weak-coupling regime, we find a quantum phase transition as function of inter-impurity hopping driven by the charge degrees of freedom. For large values of the local Coulomb repulsion, the transition is driven instead by a competition between local and non-local magnetic correlations. We find evidence that, in contrast to the usual phenomenological picture, it seems to be the bare effective exchange interactions which trigger the observed transition.
The $1994$ first discovery of a metal-insulator transition in two dimensions and series of $1997-1998$ experiments on two dimensional metal-insulator transitions in various samples of MOSFETs changed the paradigm of Anderson localization that metals cannot exist in two dimensions. Unfortunately, this delocalization physics of the diffusive regime does not apply to the effective hydrodynamic regime of quantum criticality. In the present study, we investigate effects of mutual correlations between hydrodynamic fluctuations and weak-localization corrections on Anderson localization, based on the renormalization group analysis up to the two-loop order. As a result, we find that the absence of quantum coherence in two-particle composite excitations gives rise to a novel disordered non-Fermi liquid metallic state near two dimensional nematic quantum criticality with nonmagnetic disorders. This research would be the first step in understanding the $T-$linear electrical resistivity as a characteristic feature of non-Fermi liquids and the origin of unconventional superconductivity from effective hydrodynamics of quantum criticality.
The quantum criticality of the two-lead two-channel pseudogap Anderson model is studied. Based on the non-crossing approximation, we calculate both the linear and nonlinear conductance of the model at finite temperatures with a voltage bias and a power-law vanishing conduction electron density of states, $propto |omega-mu_F|^r$ ($0<r<1$) near the Fermi energy. Equilibrium and non-equilibrium quantum critical properties at the two-channel Kondo (2CK) to local moment (LM) phase transition are addressed by extracting universal scaling functions in both linear and non-linear conductances, respectively. Clear distinctions are found on the critical exponents between linear and non-linear conductance. The implications of these two distinct quantum critical properties for the non-equilibrium quantum criticality in general are discussed.
We investigate the behavior of the periodic Anderson model in the presence of $d$-$f$ Coulomb interaction ($U_{df}$) using mean-field theory, variational calculation, and exact diagonalization of finite chains. The variational approach based on the Gutzwiller trial wave function gives a critical value of $U_{df}$ and two quantum critical points (QCPs), where the valence susceptibility diverges. We derive the critical exponent for the valence susceptibility and investigate how the position of the QCP depends on the other parameters of the Hamiltonian. For larger values of $U_{df}$, the Kondo regime is bounded by two first-order transitions. These first-order transitions merge into a triple point at a certain value of $U_{df}$. For even larger $U_{df}$ valence skipping occurs. Although the other methods do not give a critical point, they support this scenario.
The density matrix renormalization group method is applied to obtain the ground state phase diagram of the single impurity Anderson model on the honeycomb lattice at half filling. The calculation of local static quantities shows that the phase diagram contains two distinct phases, the local moment (LM) phase and the asymmetric strong coupling (ASC) phase. These results are supported by the local spin and charge excitation spectra, which exhibit qualitatively different behavior in these two phases and also reveal the existence of the valence fluctuating point at the phase boundary. For comparison, we also study the low-energy effective pseudogap Anderson model. Although the high-energy excitations are obviously different, we find that the ground state phase diagram and the asymptotically low-energy excitations are in good quantitative agreement with those for the single impurity Anderson model on the honeycomb lattice, thus providing the first quantitative justification for the previous studies based on low-energy approximate approaches. Furthermore, we find that the lowest entanglement level is doubly degenerate for the LM phase, whereas it is singlet for the ASC phase and is accidentally three fold degenerate at the valence fluctuating point. Our results therefore clearly demonstrate that the low-lying entanglement spectrum can be used to determine with high accuracy the phase boundary of the impurity quantum phase transition.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
