Local moment phases in quantum impurity problems

Minsoo Kim, Jeongmin Shim, H.-S. Sim +1 more

When a local impurity spin interacts with conduction electrons whose density of states (DOS) has a (pseudo)gap or diverges at the Fermi energy, a local moment (LM) phase can be favored over a Kondo phase. Theoretically studying quantum entanglement between the impurity and conduction electrons, we demonstrate that conduction electrons form an LM spin cloud in general LM phases, which corresponds to, but has a fundamental difference from, the Kondo cloud screening the impurity spin in the Kondo phase. The LM cloud algebraically decays over the distance from the impurity when the DOS has a pseudogap or divergence, and exponentially when it has a hard gap. We find an LM cloud length, a single length scale characterizing a universal form of the LM cloud. The findings are supported by both analytic theories and numerical computations.

Sergey Bravyi, David Gosset

Gergely Zaránd

Matthias Vojta C, R. Bulla

We discuss the dynamics of magnetic moments in d-wave superconductors. In particular, we focus on moments induced by doping nonmagnetic impurities into cuprates. The interaction of such moments with the Bogoliubov quasiparticles of the superconductors can be described by variants of the pseudogap Kondo model, characterized by a power-law density of states at the Fermi level. The numerical renormalization-group technique is employed to investigate this Kondo problem for realistic band structures and particle-hole asymmetries, both at zero and finite temperatures. In particular, we study the boundary quantum phase transition between the local-moment and asymmetric strong-coupling phases, and argue that this transition has been observed in recent nuclear magnetic resonance experiments. We determine the spectral properties of both phases and the location of the critical point as a function of Kondo coupling and doping, and discuss quantum-critical crossovers near this phase transition. In addition, changes in the local density of states around the impurity are calculated as functions of temperature, being relevant to scanning tunneling microscopy experiments.

Christian Kleine, Julian Mußhoff, Frithjof B. Anders

The energy-dependent scattering of fermions from a localized orbital at an energy-dependent rate $\ensuremath{\Gamma}(\ensuremath{\varepsilon})\ensuremath{\propto}{|\ensuremath{\varepsilon}|}^{r}$ gives rise to quantum critical points (QCPs) in the pseudogap single-impurity Anderson model separating a local moment phase with an unscreened spin moment from a strong-coupling phase which slightly deviates from the screened phase of standard Kondo problem. Using the time-dependent numerical renormalization group (TD-NRG) approach we show that local dynamic properties always equilibrate towards a steady-state value even for quenches across the QCP but with systematic deviations from the thermal equilibrium depending on the distance to the critical coupling. Local nonequilibrium properties are presented for interaction quenches and hybridization quenches. We augment our numerical data by an analytical calculation that becomes exact at short times and find excellent agreement between the numerics and the analytical theory. For interaction quenches within the screened phase we find a universal function for the time-dependent local double occupancy. We trace back the discrepancy between our results and the data obtained by a time-dependent Gutzwiller variational approach to restrictions of the wave-function ansatz in the Gutzwiller theory: while the NRG ground states properly account for the formation of an extended spin moment which decouples from the system in the unscreened phase, the Gutzwiller ansatz only allows the formation of the spin moment on the local impurity orbital.

Arne Ludwig