Impurity Quantum Phase Transitions

We review recent work on continuous quantum phase transitions in impurity models, both with fermionic and bosonic baths - these transitions are interesting realizations of boundary critical phenomena at zero temperature. The models with fermion bath are generalizations of the standard Kondo model, with the common feature that Kondo screening of the localized spin can be suppressed due to competing processes. The models with boson bath are related to the spin-boson model of dissipative two-level systems, where the interplay between tunneling and friction results in multiple phases. The competition inherent to all models can generate unstable fixed points associated with quantum phase transitions, where the impurity properties undergo qualitative changes. Interestingly, certain impurity transitions feature both lower-critical and upper-critical "dimensions" and allow for epsilon-type expansions. We present results for a number of observables, obtained by both analytical and numerical renormalization group techniques, and make connections to experiments.Comment: 22 pages, 11 figs, review article to be published in Phil. Ma

Electrical Conductivity of Fermi Liquids. II. Quasiparticle Transport

We develop a general theory of Fermi liquids to discuss the Kadowaki-Woods relation $A\propto \gamma^2$. We derive a formula for the ratio $A/\gamma^2$ which is expressed as a product of two dimensionless parameters $\alpha$ and $F$, where $\alpha$ represents a coupling constant for quasiparticle scattering and $F$ is a geometric factor determined by the shape of the Fermi surface. Then we argue that the universal ratio observed in heavy fermion compounds is reproduced under the conditions $\alpha\sim 1$ and $F\sim 20$. The former is regarded as a universality of Fermi liquids in a strong coupling regime, and the latter is corroborated by evaluating $F$ definitely in simple cases. It is noted that the proportional relation is just an example of the universal phenomena to be expected for the whole class of strong coupling Fermi liquids.Comment: 28 pages, 7 figures; J. Phys. Soc. Jpn. Vol.67, No.1

Towards first-principles understanding of the metal-insulator transition in fluid alkali metals

By treating the electron-ion interaction as perturbation in the first-principles Hamiltonian, we have calculated the density response functions of a fluid alkali metal to find an interesting charge instability due to anomalous electronic density fluctuations occurring at some finite wave vector {\bi Q} in a dilute fluid phase above the liquid-gas critical point. Since |{\bi Q}| is smaller than the diameter of the Fermi surface, this instability necessarily impedes the electric conduction, implying its close relevance to the metal-insulator transition in fluid alkali metals.Comment: 11 pages, 5 figure

Electrical Conductivity of Fermi Liquids. I. Many-body Effect on the Drude Weight

On the basis of the Fermi liquid theory, we investigate the many-body effect on the Drude weight. In a lattice system, the Drude weight $D$ is modified by electron-electron interaction due to Umklapp processes, while it is not renormalized in a Galilean invariant system. This is explained by showing that the effective mass $m'$ for $D\propto n/m'$ is defined through the current, not velocity, of quasiparticle. It is shown that the inequality $D>0$ is required for the stability against the uniform shift of the Fermi surface. The result of perturbation theory applied for the Hubbard model indicates that $D$ as a function of the density $n$ is qualitatively modified around half filling $n\sim 1$ by Umklapp processes.Comment: 20 pages, 2 figures; J. Phys. Soc. Jpn. Vol.67, No.

Praktična sinteza regulatora za precizno pozicioniranje sustava pomične podloge

This paper presents a practical feedback controller design of a ball screw-driven table system for the microdisplacement positioning. Friction of the mechanism in the micro-displacement region has nonlinear elastic properties, unlike Coulomb and/or viscous friction in the macro-displacement, resulting in different positioning responses and frequency characteristics of the plant depending on the regions. In this paper, at first, a numerical simulator with a rolling friction model is adopted to reproduce the positioning behaviors in the micro-displacement region. Based on the simulator, the stability condition of positioning in the region is clarified on the basis of frequency characteristics and, then, appropriate parameters of feedback controller are practically designed to satisfy the required positioning performance. Effectiveness of the proposed design has been verified by a series of experiments using a prototype of ball screw-driven table positioning device.U radu je prikazana sinteza regulatora s povratnom vezom u sustavu za precizno linearno pozicioniranje pomične podloge pomoću kugličnih ležajeva. Za razliku od uobičajenih modela Coulombova i/ili viskoznog trenja, trenje razmatranog sustava ima izrazito nelinearna svojstva u području mikro-pomaka, što za posljedicu ima različite odzive pozicioniranja i frekvencijski karakteristike, ovisno o radnom području. U radu je prvo razvijeno numeričko simulacijsko okruženje zasnovano na modelu trenja kotrljanja u svrhu simuliranja ponašanja sustava pozicioniranja u području mikropomaka. Potom je, zasnivajući se na simulacijskom okruženju, pomoću frekvencijske karakteristike razjašnjen problem stabilnosti sustava u promatranom radnom području te su odabrani odgovarajući parametri regulatora koji poštuju uvjet stabilnosti i zadovoljavaju željenu kvalitetu odziva. Sinteza regulatora provedena je vodeći računa o praktičnoj primjenjivosti postupka. Učinkovitost predložene sinteze potvr.ena je nizom eksperimenata na prototipu sustava za precizno linearno pozicioniranje pomične podloge pomoću kugličnih ležajeva

Coupled CDW and SDW Fluctuations as an Origin of Anomalous Properties of Ferromagnetic Superconductor UGe_2

It is shown that anomalous properties of UGe_2 can be understood in a unified way on the basis of a single assumption that the superconductivity is mediated by the coupled SDW and CDW fluctuations induced by the imperfect nesting of the Fermi surface with majority spins at T=T_x(P) deep in the ferromagnetic phase. Excess growth of uniform magnetization is shown to develop in the temperature range T<T_x(P) as a mode-coupling effect of coupled growth of SDW and CDW orderings, which has been observed by two different types of experiments. The coupled CDW and SDW fluctuations are shown to be essentially ferromagnetic spin fluctuations which induce a spin-triplet p-wave attraction. These fluctuations consist of two modes, spin and charge fluctuations with large momentum transfer of the nesting vector. An anomalous temperature dependence of the upper critical field H_c2(T) such as crossing of H_c2(T) at P=11.4 kbar and P=13.5 kbar, can be understood by the strong-coupling-superconductivity formalism. Temperature dependence of the lattice specific heat including a large shoulder near T_x is also explained quite well as an effect of a kind of Kohn anomaly associated with coupled SDW-CDW transition.Comment: (12 pages, 10 eps figures) submitted to J. Phys. Soc. Jp

Singular Effects of Impurities near the Ferromagnetic Quantum-Critical Point

Systematic theoretical results for the effects of a dilute concentration of magnetic impurities on the thermodynamic and transport properties in the region around the quantum critical point of a ferromagnetic transition are obtained. In the quasi-classical regime, the dynamical spin fluctuations enhance the Kondo temperature. This energy scale decreases rapidly in the quantum fluctuation regime, where the properties are those of a line of critical points of the multichannel Kondo problem with the number of channels increasing as the critical point is approached, except at unattainably low temperatures where a single channel wins out.Comment: 4 pages, 2 figure

Effect of Umklapp Scattering on Magnetic Field Penetration Depth in High-Tc Cuprates

The renormalization of the magnetic field penetration depth $\lambda$ owing to the electron-electron correlation is discussed with its application to high-$T_{\rm c}$ cuprates. The formula for the current carried by quasiparticle with the Umklapp scattering is derived, on the basis of which we investigate how the value of $\lambda^{-2}$ deviates from that of $n/m^*$ where $n$ and $m^*$ are the carrier density and the effective mass respectively. Although this deviation is small in the case of weak momentum dependence of the vertex, this is large and negative owing to the non-negligible value of the backflow in the case of the strong antiferromagnetic spin fluctuation. The observed doping dependence of $\lambda^{-2}$ in high-$T_{\rm c}$ cuprates, specifically a peak structure at the slightly overdoped region, is explained by the analytical consideration and the numerical calculation based on the perturbation theory and the spin fluctuation theory. The consistency between $\lambda^{-2}$ and ${\rm d}\lambda^{-2}/{\rm d}T$ at absolute zero, which is the problem the isotropic model fails to explain, is also obtained by our theory.Comment: 25 pages, 9 figures. Another version(11 pages longer) will appear in J. Phys. Soc. Jpn (2002) No.