A fractional-spin phase in the power-law Kondo model

We consider a Kondo impurity coupled to a fermionic host with a power-law density of states near the Fermi level, rho(epsilon) ~ |epsilon|^r, with exponent r<0. Using both perturbative renormalization group (poor man's scaling) and numerical renormalization group methods, we analyze the phase diagram of this model for ferromagnetic and antiferromagnetic Kondo coupling. Both sectors display non-trivial behavior with several stable phases separated by second-order transitions. In particular, on the ferromagnetic side there is a stable intermediate-coupling fixed point with universal properties corresponding to a fractional ground-state spin.Comment: 5 pages, 4 figs; (v2) extended discussion and added refs; final version as publishe

Critical quasiparticles in single-impurity and lattice Kondo models

Quantum criticality in systems of local moments interacting with itinerant electrons has become an important and diverse field of research. Here we review recent results which concern (a) quantum phase transitions in single-impurity Kondo and Anderson models and (b) quantum phase transitions in heavy-fermion lattice models which involve critical quasiparticles. For (a) the focus will be on impurity models with a pseudogapped host density of states and their applications, e.g., in graphene and other Dirac materials, while (b) is devoted to strong-coupling behavior near antiferromagnetic quantum phase transitions, with potential applications in a variety of heavy-fermion metals.Comment: 18 pages, 4 figs, mini-review. arXiv admin note: text overlap with arXiv:1208.311

Gate-controlled Kondo screening in graphene: Quantum criticality and electron-hole asymmetry

Magnetic impurities in neutral graphene provide a realization of the pseudogap Kondo model, which displays a quantum phase transition between phases with screened and unscreened impurity moment. Here, we present a detailed study of the pseudogap Kondo model with finite chemical potential mu. While carrier doping restores conventional Kondo screening at lowest energies, properties of the quantum critical fixed point turn out to influence the behavior over a large parameter range. Most importantly, the Kondo temperature T_K shows an extreme asymmetry between electron and hole doping. At criticality, depending on the sign of mu, T_K follows either the scaling prediction T_K ~ |mu| with a universal prefactor, or T_K ~ |mu|^x with x = 2.6. This asymmetry between electron and hole doping extends well outside the quantum critical regime and also implies a qualitative difference in the shape of the tunneling spectra for both signs of mu.Comment: 6 pages, 6 figs; (v2) extended discussion of RG flow, final version as publishe

Equilibrium and non-equilibrium dynamics of the sub-ohmic spin-boson model

Employing the non-perturbative numerical renormalization group method, we study the dynamics of the spin-boson model, which describes a two-level system coupled to a bosonic bath with spectral density J(omega) propto omega^s. We show that, in contrast to the case of ohmic damping, the delocalized phase of the sub-ohmic model cannot be characterized by a single energy scale only, due to the presence of a non-trivial quantum phase transition. In the strongly sub-ohmic regime, s<<1, weakly damped coherent oscillations on short time scales are possible even in the localized phase - this is of crucial relevance, e.g., for qubits subject to electromagnetic noise.Comment: 4 pages, 6 figures; final version, as publishe

Real-space renormalization group flow in quantum impurity systems: local moment formation and the Kondo screening cloud

The existence of a length-scale $\xi_K\sim 1/T_K$ (with $T_K$ the Kondo temperature) has long been predicted in quantum impurity systems. At low temperatures $T\ll T_K$, the standard interpretation is that a spin-$\tfrac{1}{2}$ impurity is screened by a surrounding `Kondo cloud' of spatial extent $\xi_K$. We argue that renormalization group (RG) flow between any two fixed points (FPs) results in a characteristic length-scale, observed in real-space as a crossover between physical behaviour typical of each FP. In the simplest example of the Anderson impurity model, three FPs arise; and we show that `free orbital', `local moment' and `strong coupling' regions of space can be identified at zero temperature. These regions are separated by two crossover length-scales $\xi_{\text{LM}}$ and $\xi_K$, with the latter diverging as the Kondo effect is destroyed on increasing temperature through $T_K$. One implication is that moment formation occurs inside the `Kondo cloud', while the screening process itself occurs on flowing to the strong coupling FP at distances $\sim \xi_K$. Generic aspects of the real-space physics are exemplified by the two-channel Kondo model, where $\xi_K$ now separates `local moment' and `overscreening' clouds.Comment: 6 pages; 5 figure

Charge ordering and phase separation in the infinite dimensional extended Hubbard model

We study the extended Hubbard model with both on-site (U) and nearest neighbor (V) Coulomb repulsion using the exact diagonalization method within the dynamical mean field theory. For a fixed U (U=2.0), the T-n phase-diagrams are obtained for V=1.4 and V=1.2, at which the ground states of n=1/2 system is charge-ordered and charge-disordered, respectively. In both cases, robust charge order is found at finite temperature and in an extended filling regime around n=1/2. The order parameter changes non-monotonously with temperature. For V=1.4, phase separation between charge-ordered and charge-disordered phases is observed in the low temperature and n < 0.5 regime. It is described by an "S"-shaped structure of the n-/mu curve. For V=1.2, the ground state is charge-disordered, and a reentrant charge-ordering transition is observed for 0.42 < n < 0.68. Relevance of our results to experiments for doped manganites is discussed.Comment: 9 pages, 7 figures, submitted to Phys. Rev.

Quantum phase transitions and thermodynamics of the power-law Kondo model

We revisit the physics of a Kondo impurity coupled to a fermionic host with a diverging power-law density of states near the Fermi level, $\rho(\omega) \sim |\omega|^r$, with exponent $-1<r<0$. Using the analytical understanding of several fixed points, based partially on powerful mappings between models with bath exponents $r$ and $(-r)$, combined with accurate numerical renormalization group calculations, we determine thermodynamic quantities within the stable phases, and also near the various quantum phase transitions. Antiferromagnetic Kondo coupling leads to strong screening with a negative zero-temperature impurity entropy, while ferromagnetic Kondo coupling can induce a stable fractional spin moment. We formulate the quantum field theories for all critical fixed points of the problem, which are fermionic in nature and allow for a perturbative renormalization-group treatment.Comment: 13 pages, 11 figure

Numerical Renormalization Group for Impurity Quantum Phase Transitions: Structure of Critical Fixed Points

The numerical renormalization group method is used to investigate zero temperature phase transitions in quantum impurity systems, in particular in the particle-hole symmetric soft-gap Anderson model. The model displays two stable phases whose fixed points can be built up of non-interacting single-particle states. In contrast, the quantum phase transitions turn out to be described by interacting fixed points, and their excitations cannot be described in terms of free particles. We show that the structure of the many-body spectrum of these critical fixed points can be understood using renormalized perturbation theory close to certain values of the bath exponents which play the role of critical dimensions. Contact is made with perturbative renormalization group calculations for the soft-gap Anderson and Kondo models. A complete description of the quantum critical many-particle spectra is achieved using suitable marginal operators; technically this can be understood as epsilon-expansion for full many-body spectra.Comment: 14 pages, 12 figure

Numerical Renormalization Group for Bosonic Systems and Application to the Subohmic Spin-Boson Model

We describe the generalization of Wilson's Numerical Renormalization Group method to quantum impurity models with a bosonic bath, providing a general non-perturbative approach to bosonic impurity models which can access exponentially small energies and temperatures. As an application, we consider the spin-boson model, describing a two-level system coupled to a bosonic bath with power-law spectral density, J(omega) ~ omega^s. We find clear evidence for a line of continuous quantum phase transitions for subohmic bath exponents 0<s<1; the line terminates in the well-known Kosterlitz-Thouless transition at s=1. Contact is made with results from perturbative renormalization group, and various other applications are outlined.Comment: 4 pages, 5 figs, (v2) final version as publishe

Phenomenological Modeling of Photoemission Spectra in Strongly Correlated Electron Systems

A phenomenological approach is presented that allows one to model, and thereby interpret, photoemission spectra of strongly correlated electron systems. A simple analytical formula for the self-energy is proposed. This self-energy describes both coherent and incoherent parts of the spectrum (quasiparticle and Hubbard peaks, respectively). Free parameters in the expression are determined by fitting the density of states to experimental photoemission data. An explicit fitting is presented for the La$_{1-x}$Sr$_x$TiO$_3$ system with $0.08 \le x \le 0.38$. In general, our phenomenological approach provides information on the effective mass, the Hubbard interaction, and the spectral weight distribution in different parts of the spectrum. Limitations of this approach are also discussed.Comment: 13 pages, 4 figures, IJMPB style (included