Interplay between strong correlations and magnetic field in the symmetric periodic Anderson model

Magnetic field effects in Kondo insulators are studied theoretically, using a local moment approach to the periodic Anderson model within the framework of dynamical mean-field theory. Our main focus is on field-induced changes in single-particle dynamics and the associated hybridization gap in the density of states. Particular emphasis is given to the strongly correlated regime, where dynamics are found to exhibit universal scaling in terms of a field-dependent low energy coherence scale. Although the bare applied field is globally uniform, the effective fields experienced by the conduction electrons and the $f$-electrons differ because of correlation effects. A continuous insulator-metal transition is found to occur on increasing the applied field, closure of the hybridization gap reflecting competition between Zeeman splitting and screening of the $f$-electron local moments. For intermediate interaction strengths the hybridization gap depends non-linearly on the applied field, while in strong coupling its field dependence is found to be linear. For the classic Kondo insulator YbB$_{12}$, good agreement is found upon direct comparison of the field evolution of the experimental transport gap with the theoretical hybridization gap in the density of states.Comment: 8 pages, 8 figure

Dynamics and transport properties of heavy fermions: theory

The paramagnetic phase of heavy fermion systems is investigated, using a non-perturbative local moment approach to the asymmetric periodic Anderson model within the framework of dynamical mean field theory. The natural focus is on the strong coupling Kondo-lattice regime wherein single-particle spectra, scattering rates, dc transport and optics are found to exhibit w/w_L,T/w_L scaling in terms of a single underlying low-energy coherence scale w_L. Dynamics/transport on all relevant (w,T)-scales are encompassed, from the low-energy behaviour characteristic of the lattice coherent Fermi liquid, through incoherent effective single-impurity physics likewise found to arise in the universal scaling regime, to non-universal high-energy scales; and which description in turn enables viable quantitative comparison to experiment.Comment: 27 pages, 12 figure

Spectral scaling and quantum critical behaviour in the pseudogap Anderson model

The pseudogap Anderson impurity model provides a classic example of an essentially local quantum phase transition. Here we study its single-particle dynamics in the vicinity of the symmetric quantum critical point (QCP) separating generalized Fermi liquid and local moment phases, via the local moment approach. Both phases are shown to be characterized by a low-energy scale that vanishes at the QCP; and the universal scaling spectra, on all energy scales, are obtained analytically. The spectrum precisely at the QCP is also obtained; its form showing clearly the non-Fermi liquid, interacting nature of the fixed point.Comment: 7 pages, 2 figure

Dynamics and transport properties of Kondo insulators

A many-body theory of paramagnetic Kondo insulators is described, focusing specifically on single-particle dynamics, scattering rates, d.c. transport and optical conductivities. This is achieved by development of a non-perturbative local moment approach to the symmetric periodic Anderson model within the framework of dynamical mean-field theory. Our natural focus is the strong coupling, Kondo lattice regime; in particular the resultant `universal' scaling behaviour in terms of the single, exponentially small low-energy scale characteristic of the problem. Dynamics/transport on all relevant ($\omega, T$) scales are considered, from the gapped/activated behaviour characteristic of the low-temperature insulator through to explicit connection to single-impurity physics at high $\omega$ and/or $T$; and for optical conductivities emphasis is given to the nature of the optical gap, the temperature scale responsible for its destruction, and the consequent clear distinction between indirect and direct gap scales. Using scaling, explicit comparison is also made to experimental results for d.c. transport and optical conductivites of Ce_3Bi_4Pt_3, SmB_6 and YbB_{12}. Good agreement is found, even quantitatively; and a mutually consistent picture of transport and optics results.Comment: 49 pages, 23 figure

Optical and transport properties of heavy fermions: theory compared to experiment

Employing a local moment approach to the periodic Anderson model within the framework of dynamical mean-field theory, direct comparison is made between theory and experiment for the dc transport and optical conductivities of paramagnetic heavy fermion and intermediate valence metals. Four materials, exhibiting a diverse range of behaviour in their transport/optics, are analysed in detail: CeB6, YbAl3, CeAl3 and CeCoIn5. Good agreement between theory and experiment is in general found, even quantitatively, and a mutually consistent picture of transport and optics results.Comment: 21 pages, 10 figures; Replacement with minor style changes made to avoid postscript file error

Dynamics and scaling in the periodic Anderson model

The periodic Anderson model (PAM) captures the essential physics of heavy fermion materials. Yet even for the paramagnetic metallic phase, a practicable many-body theory that can simultaneously handle all energy scales while respecting the dictates of Fermi liquid theory at low energies, and all interaction strengths from the strongly correlated Kondo lattice through to weak coupling, has remained quite elusive. Aspects of this problem are considered in the present paper where a non-perturbative local moment approach (LMA) to single-particle dynamics of the asymmetric PAM is developed within the general framework of dynamical mean-field theory. All interaction strengths and energy scales are encompassed, although our natural focus is the Kondo lattice regime of essentially localized $f$-spins but general conduction band filling, characterised by an exponentially small lattice coherence scale $\omega_{L}$. Particular emphasis is given to the resultant universal scaling behaviour of dynamics in the Kondo lattice regime as an entire function of $\omega^{\prime} =\omega/\omega_{L}$, including its dependence on conduction band filling, $f$-level asymmetry and lattice type.A rich description arises, encompassing both coherent Fermi liquid behaviour at low-$\omega^{\prime}$ and the crossover to effective single-impurity scaling physics at higher energies -- but still in the $\omega/\omega_{L}$-scaling regime, and as such incompatible with the presence of two-scale `exhaustion' physics, which is likewise discussed.Comment: 22 pages in EPJB format, 14 figures; accepted for publication in EPJB; (small change in the comments section, no change in manuscript

On the complexity of resource-bounded logics

We revisit decidability results for resource-bounded logics and use decision problems on vector addition systems with states (VASS) in order to establish complexity characterisations of (decidable) model checking problems. We show that the model checking problem for the logic RB+-ATL is 2EXPTIME-complete by using recent results on alternating VASS (and in EXPTIME when the number of resources is bounded). Moreover, we establish that the model checking problem for RBTL is EXPSPACE-complete. The problem is decidable and of the same complexity for RBTL*, proving a new decidability result as a by-product of the approach. When the number of resources is bounded, the problem is in PSPACE. We also establish that the model checking problem for RB+-ATL*, the extension of RB+-ATL with arbitrary path formulae, is decidable by a reduction to parity games for single-sided VASS (a variant of alternating VASS). Furthermore, we are able to synthesise values for resource parameters. Hence, the paper establishes formal correspondences between model checking problems for resource bounded logics advocated in the AI literature and decision problems on alternating VASS, paving the way for more applications and cross-fertilizations

A spin-dependent local moment approach to the Anderson impurity model

We present an extension of the local moment approach to the Anderson impurity model with spin-dependent hybridization. By employing the two-self-energy description, as originally proposed by Logan and co-workers, we applied the symmetry restoration condition for the case with spin-dependent hybridization. Self-consistent ground states were determined through variational minimization of the ground state energy. The results obtained with our spin-dependent local moment approach applied to a quantum dot system coupled to ferromagnetic leads are in good agreement with those obtained from previous work using numerical renormalization group calculations

Magnetoresistance in paramagnetic heavy fermion metals

A theoretical study of magnetic field (h) effects on single-particle spectra and transport quantities of heavy fermion metals in the paramagnetic phase is carried out. We have employed a non-perturbative local moment approach (LMA) to the asymmetric periodic Anderson model within the dynamical mean field framework. The lattice coherence scale \om_L, which is proportional within the LMA to the spin-flip energy scale, and has been shown in earlier studies to be the energy scale at which crossover to single impurity physics occurs,increases monotonically with increasing magnetic field. The many body Kondo resonance in the density of states at the Fermi level splits into two with the splitting being proportional to the field itself. For h$\geq$ 0, we demonstrate adiabatic continuity from the strongly interacting case to a corresponding non-interacting limit, thus establishing Fermi liquid behaviour for heavy fermion metals in the presence of magnetic field. In the Kondo lattice regime, the theoretically computed magnetoresistance is found to be negative in the entire temperature range. We argue that such a result could be understood at T\gtrsim \om_L by field-induced suppression of spin-flip scattering and at T\lesssim \om_L through lattice coherence. The coherence peak in the heavy fermion resistivity diminishes and moves to higher temperatures with increasing field. Direct comparison of the theoretical results to the field dependent resistivity measurements in CeB$_6$ yields good agreement.Comment: 17 pages, 8 figure