Numerical renormalization-group study of the Bose-Fermi Kondo model

We extend the numerical renormalization-group method to Bose-Fermi Kondo models (BFKMs), describing a local moment coupled to a conduction band and a dissipative bosonic bath. We apply the method to the Ising-symmetry BFKM with a bosonic bath spectral function eta(omega) proportional omega(s), of interest in connection with heavy-fermion criticality. For 0 < s < 1, an interacting critical point, characterized by hyperscaling of exponents and omega/T scaling, describes a quantum phase transition between Kondo-screened and localized phases. A connection is made to other results for the BFKM and the spin-boson model.     

Scaling and enhanced symmetry at the quantum critical point of the sub-ohmic Bose-Fermi Kondo model

We consider the finite-temperature scaling properties of a Kondo-destroying quantum critical point in the Ising-anisotropic Bose-Fermi Kondo model (BFKM). A cluster-updating Monte Carlo approach is used, in order to reliably access a wide temperature range. The scaling function for the two-point spin correlator is found to have the form dictated by a boundary conformal field theory, even though the underlying Hamiltonian lacks conformal invariance. Similar conclusions are reached for all multipoint correlators of the spin-isotropic BFKM in a dynamical large-N limit. Our results suggest that the quantum critical local properties of the sub-Ohmic BFKM are those of an underlying boundary conformal field theory.     

Zero-temperature magnetic transition in an easy-axis Kondo lattice model

We address the quantum transition of a spin-1/2 antiferromagnetic Kondo lattice model with an easy-axis anisotropy using the extended dynamical mean field theory. We derive results in real frequency by using the bosonic numerical renormalization group (BNRG) method and compare them with quantum Monte Carlo results in Matsubara frequency. The BNRG results show a logarithmic divergence in the critical local spin susceptibility, signaling a destruction of Kondo screening. The T=0 transition is consistent with being second order. The BNRG results also display some subtle features; we identify their origin and suggest means for further microscopic studies.     

Kondo effect in bosonic spin liquids

In a metal, a magnetic impurity is fully screened by the conduction electrons at low temperature. In contrast, impurity moments coupled to spin-1 bulk bosons, such as triplet excitations in paramagnets, are only partially screened, even at the bulk quantum critical point. We argue that this difference is not due to the quantum statistics of the host particles but instead related to the structure of the impurity-host coupling, by demonstrating that frustrated magnets with bosonic spinon excitations can display a bosonic version of the Kondo effect. However, the Bose statistics of the bulk implies distinct behavior, such as a weak-coupling impurity quantum phase transition, and perfect screening for a range of impurity spin values. We discuss implications of our results for the compound Cs2CuCl4, as well as possible extensions to multicomponent bosonic gases.     

Pseudogap Fermi-Bose Kondo model

We consider a magnetic impurity coupled to both fermionic quasiparticles with a pseudogap density of states and bosonic spin fluctuations. Using renormalization group and large-N calculations we investigate the phase diagram of the resulting Fermi-Bose Kondo model. We show that the Kondo temperature is strongly reduced by low-energy spin fluctuations, and make connections to experiments in cuprate superconductors. Furthermore, we derive an exact exponent for the critical behavior of the conduction electron T matrix, and propose our findings to be relevant for certain scenarios of local quantum criticality in heavy-fermion metals.     

Critical Kondo destruction and the violation of the quantum-to-classical mapping of quantum criticality

Antiferromagnetic heavy fermion metals close to their quantum critical points display a richness in their physical properties unanticipated by the traditional approach to quantum criticality, which describes the critical properties solely in terms of fluctuations of the order parameter. This has led to the question as to how the Kondo effect gets destroyed as the system undergoes a phase change. In one approach to the problem, Kondo lattice systems are studied through a self-consistent Bose-Fermi Kondo model within the extended dynamical mean field theory. The quantum phase transition of the Kondo lattice is thus mapped onto that of a sub-Ohmic Bose-Fermi Kondo model. In the present article we address some aspects of the failure of the standard order-parameter functional for the Kondo-destroying quantum critical point of the Bose-Fermi Kondo model.     

Continuous quantum phase transition in a Kndo lattice model

We study the magnetic quantum phase transition in an anisotropic Kondo lattice model. The dynamical competition between the RKKY and Kondo interactions is treated using an extended dynamic mean field theory appropriate for both the antiferromagnetic and paramagnetic phases. A quantum Monte Carlo approach is used, which is able to reach very low temperatures, of the order of 1% of the bare Kondo scale. We find that the finite-temperature magnetic transition, which occurs for sufficiently large RKKY interactions, is first order. The extrapolated zero-temperature magnetic transition, on the other hand, is continuous and locally critical.     

Stripes, topological order, and deconfinement in a planar t-Jz model

We determine the quantum phase diagram of a two-dimensional bosonic t-Jz model as a function of the lattice anisotropy gamma, using a quantum Monte Carlo loop algorithm. We show analytically that the low-energy sectors of the bosonic and the fermionic t-Jz models become equivalent in the limit of small gamma. In this limit, the ground state represents a static stripe phase characterized by a nonzero value of a topological order parameter. This phase remains up to intermediate values of gamma, where there is a quantum phase transition to a phase-segregated state or a homogeneous superfluid with dynamic stripe fluctuations depending on the ratio Jz/t.     

Fermi surface and antiferromagnetism in the Kondo lattice: an asymptotically exact solution in d>1 dimensions

Interest in the heavy fermion metals has motivated us to examine the quantum phases and their Fermi surfaces within the Kondo lattice model. We demonstrate that the model is soluble asymptotically exactly in any dimension d>1, when the Kondo coupling is small compared with the RKKY interaction and in the presence of antiferromagnetic ordering. We show that the Kondo coupling is exactly marginal in the renormalization group sense, establishing the stability of an ordered phase with a small Fermi surface AFS. Our results have implications for the global phase diagram of the heavy fermion metals, suggesting a Lifshitz transition inside the antiferromagnetic region and providing a new perspective for a Kondo-destroying antiferromagnetic quantum critical point.     

Magnetic quantum phase transition in an anisotropic kondo lattice

The quantum phase transition between paramagnetic and antiferromagnetic phases of the Kondo lattice model with Ising anisotropy in the intersite exchange is studied within extended dynamical mean-field theory. Nonperturbative numerical solutions at zero temperature point to a continuous transition for both two- and three-dimensional magnetism. In the former case, the transition is associated with critical local physics, characterized by a vanishing Kondo scale and by an anomalous exponent in the dynamics close in value to that measured in heavy-fermion CeCu5.9Au0.1.     

Fermi-surface reconstruction without breakdown of Kondo screening at the quantum critical point

Motivated by recent Hall-effect experiment in YbRh(2)Si(2), we study ground state properties of a Kondo lattice model in a two-dimensional square lattice using variational Monte Carlo method. We show that there are two types of phase transition, an antiferromagnetic transition and a topological one (Fermi-surface reconstruction). In a wide region of parameters, these two transitions occur simultaneously without the breakdown of Kondo screening, accompanied by a discontinuous change of the Hall coefficient. This result is consistent with the experiment and gives a novel theoretical picture for the quantum critical point in heavy-fermion systems.     

Competition between Kondo and RKKY correlations in the presence of strong randomness

We propose that competition between Kondo and magnetic correlations results in a novel universality class for heavy fermion quantum criticality in the presence of strong randomness. Starting from an Anderson lattice model with disorder, we derive an effective local field theory in the dynamical mean-field theory approximation, where randomness is introduced into both hybridization and Ruderman-Kittel-Kasuya-Yosida (RKKY) interactions. Performing the saddle-point analysis in the U(1) slave-boson representation, we reveal its phase diagram which shows a quantum phase transition from a spin liquid state to a local Fermi liquid phase. In contrast with the clean limit case of the Anderson lattice model, the effective hybridization given by holon condensation turns out to vanish, resulting from the zero mean value of the hybridization coupling constant. However, we show that the holon density becomes finite when the variance of the hybridization is sufficiently larger than that of the RKKY coupling, giving rise to the Kondo effect. On the other hand, when the variance of the hybridization becomes smaller than that of the RKKY coupling, the Kondo effect disappears, resulting in a fully symmetric paramagnetic state, adiabatically connected to the spin liquid state of the disordered Heisenberg model. We investigate the quantum critical point beyond the mean-field approximation. Introducing quantum corrections fully self-consistently in the non-crossing approximation, we prove that the local charge susceptibility has exactly the same critical exponent as the local spin susceptibility, suggesting an enhanced symmetry at the local quantum critical point. This leads us to propose novel duality between the Kondo singlet phase and the critical local moment state beyond the Landau-Ginzburg-Wilson paradigm. The Landau-Ginzburg-Wilson forbidden duality serves the mechanism of electron fractionalization in critical impurity dynamics, where such fractionalized excitations are identified with topological excitations.     

Entanglement entropy, decoherence, and quantum phase transitions of a dissipative two-level system

The concept of entanglement entropy appears in multiple contexts, from black hole physics to quantum information theory, where it measures the entanglement of quantum states. We investigate the entanglement entropy in a simple model, the spin-boson model, which describes a qubit (two-level system) interacting with a collection of harmonic oscillators that models the environment responsible for decoherence and dissipation. The entanglement entropy allows to make a precise unification between entanglement of the spin with its environment, decoherence, and quantum phase transitions. We derive exact analytical results which are confirmed by Numerical Renormalization Group arguments both for an ohmic and a subohmic bosonic bath. The entanglement entropy obeys universal scalings. We make comparisons with entanglement properties in the quantum Ising model and in the Dicke model. We also emphasize the possibility of measuring this entropy using charge qubits subject to electromagnetic noise; such measurements would provide an empirical proof of the existence of entanglement entropy.     

Kondo breakdown as a selective Mott transition in the Anderson lattice

We show within the slave-boson technique that the Anderson lattice model exhibits a Kondo breakdown quantum critical point where the hybridization goes to zero at zero temperature. At this fixed point, the f electrons experience as well a selective Mott transition separating a local-moment phase from a Kondo-screened phase. The presence of a multiscale quantum critical point in the Anderson lattice in the absence of magnetism is discussed in the context of heavy fermion compounds. This study is the first evidence for a selective Mott transition in the Anderson lattice.     

Quantum phase transitions in the bosonic single-impurity Anderson model

We consider a quantum impurity model in which a bosonic impurity level is coupled to a non-interacting bosonic bath, with the bosons at the impurity site subject to a local Coulomb repulsion U. Numerical renormalization group calculations for this bosonic single-impurity Anderson model reveal a zero-temperature phase diagram where Mott phases with reduced charge fluctuations are separated from a Bose-Einstein condensed phase by lines of quantum critical points. We discuss possible realizations of this model, such as atomic quantum dots in optical lattices. Furthermore, the bosonic single-impurity Anderson model appears as an effective impurity model in a dynamical mean-field theory of the Bose-Hubbard model.     

Half-filled Kondo lattice on the honeycomb lattice

The unique linear density of state around the Dirac points for the honeycomb lattice brings much novel features in strongly correlated models. Here we study the ground-state phase diagram of the Kondo lattice model on the honeycomb lattice at half-filling by using an extended mean-field theory. By treating magnetic interaction and Kondo screening on an equal footing, it is found that besides a trivial discontinuous first-order quantum phase transition between well-defined Kondo insulator and antiferromagnetic insulating state, there can exist a wide coexistence region with both Kondo screening and antiferromagnetic orders in the intermediate coupling regime. In addition, the stability of Kondo insulator requires a minimum strength of the Kondo coupling. These features are attributed to the linear density of state, which are absent in the square lattice. Furthermore, fluctuation effect beyond the mean-field decoupling is analyzed and the corresponding antiferromagnetic spin-density-wave transition falls into the O(3) universal class. Comparatively, we also discuss the Kondo necklace and the Kane-Mele-Kondo (KMK) lattice models on the same lattice. Interestingly, it is found that the topological insulating state is unstable to the usual antiferromagnetic ordered states at half-filling for the KMK model. The present work may be helpful for further study on the interplay between conduction electrons and the densely localized spins on the honeycomb lattice.     

Absence of single-particle Bose-Einstein condensation at low densities for bosons with correlated hopping

Motivated by the physics of mobile triplets in frustrated quantum magnets, the properties of a two-dimensional model of bosons with correlated hopping are investigated. A mean-field analysis reveals the presence of a pairing phase without single-particle Bose-Einstein condensation (BEC) at low densities for sufficiently strong correlated hopping, and of an Ising quantum phase transition towards a BEC phase at larger density. The physical arguments supporting the mean-field results and their implications for bosonic and quantum spin systems are discussed.     

Field induced magnetic ordering transition in Kondo insulators

We study the 2D Kondo insulators in a uniform magnetic field using quantum Monte Carlo simulations of the particle-hole symmetric Kondo lattice model and a mean field analysis of the Periodic Anderson model. We find that the field induces a transition to an insulating, antiferromagnetically ordered phase with staggered moment in the plane perpendicular to the field. For fields in excess of the quasi-particle gap, corresponding to a metal in a simple band picture of the periodic Anderson model, we find that the metallic phase is unstable towards the spin density wave type ordering for any finite value of the interaction strength. This can be understood as a consequence of the perfect nesting of the particle and hole Fermi surfaces that emerge as the field closes the gap. We propose a phase diagram and investigate the quasi-particle and charge excitations in the magnetic field. We find good agreement between the mean-field and quantum Monte Carlo results.Received: 17 December 2003, Published online: 8 June 2004PACS: 71.27. + a Strongly correlated electron systems; heavy fermions - 71.10.Fd Lattice fermion models (Hubbard model, etc.) - 71.30. + h Metal-insulator transitions and other electronic transitions - 75.30.Mb Valence fluctuation, Kondo lattice, and heavy-fermion phenomena - 75.30.Fv Spin-density waves     

Numerical renormalization group for bosonic systems and application to the sub-ohmic 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 nonperturbative 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) proportional to omega(s). We find clear evidence for a line of continuous quantum phase transitions for sub-Ohmic bath exponents 0相似文献   

Effect of a fermion on quantum phase transitions in bosonic systems

The effect of a fermion with angular momentum j on quantum phase transitions of a (s,d) bosonic system is investigated. It is shown that the presence of a fermion strongly modifies the critical value at which the transition occurs, and its nature, even for small and moderate values of the coupling constant. The analogy with a bosonic system in an external field is mentioned. Experimental evidence for precursors of quantum phase transitions in bosonic systems plus a fermion (odd-even nuclei) is presented.