Quadrupole Susceptibility of Gd-Based Filled Skutterudite Compounds

It is shown that quadrupole susceptibility can be detected in Gd compounds contrary to our textbook knowledge that Gd$^{3+}$ ion induces pure spin moment due to the Hund's rules in an $LS$ coupling scheme. The ground-state multiplet of Gd$^{3+}$ is always characterized by $J$=7/2, where $J$ denotes total angular momentum, but in a $j$-$j$ coupling scheme, one $f$ electron in $j$=7/2 octet carries quadrupole moment, while other six electrons fully occupy $j$=5/2 sextet, where $j$ denotes one-electron total angular momentum. For realistic values of Coulomb interaction and spin-orbit coupling, the ground-state wavefunction is found to contain significant amount of the $j$-$j$ coupling component. From the evaluation of quadrupole susceptibility in a simple mean-field approximation, we point out a possibility to detect the softening of elastic constant in Gd-based filled skutterudites.Comment: 8 pages, 4 figure

Electric Dipolar Susceptibility of the Anderson-Holstein Model

The temperature dependence of electric dipolar susceptibility \chi_P is discussed on the basis of the Anderson-Holstein model with the use of a numerical renormalization group (NRG) technique. Note that P is related with phonon Green's function D. In order to obtain correct temperature dependence of P at low temperatures, we propose a method to evaluate P through the Dyson equation from charge susceptibility \chi_c calculated by the NRG, in contrast to the direct NRG calculation of D. We find that the irreducible charge susceptibility estimated from \chi_c agree with the perturbation calculation, suggesting that our method works well.Comment: 4 pages, 4 figure

Electron Mass Enhancement due to Anharmonic Local Phonons

In order to understand how electron effective mass is enhanced by anharmonic local oscillation of an atom in a cage composed of other atoms, i.e., {\it rattling}, we analyze anharmonic Holstein model by using a Green's function method. Due to the evaluation of an electron mass enhancement factor $Z$, we find that $Z$ becomes maximum when zero-point energy is comparable with potential height at which the amplitude of oscillation is rapidly enlarged. Cooperation of such quantum and rattling effects is considered to be a key issue to explain the electron mass enhancement in electron-rattling systems.Comment: 3 pages, 3 figures, to appear in J. Phys. Soc. Jpn. Suppl. (Proceedings for International Conference on Heavy Electrons

Kondo Effect in an Electron System with Dynamical Jahn-Teller Impurity

We investigate how Kondo phenomenon occurs in the Anderson model dynamically coupled with local Jahn-Teller phonons. It is found that the total angular moment composed of electron pseudo-spin and phonon angular moments is screened by conduction electrons. Namely, phonon degrees of freedom essentially contribute to the formation of singlet ground state. A characteristic temperature of the Kondo effect due to dynamical Jahn-Teller phonons is explained by an effective $s$-$d$ Hamiltonian with anisotropic exchange interaction obtained from the Jahn-Teller-Anderson model in a non-adiabatic region.Comment: 5 pages, 3 figure

Filling dependence of a new type of charge ordered liquid on a triangular lattice system

We study the recently reported characteristic gapless charge ordered state in a spinless fermion system on a triangular lattice under strong inter-site Coulomb interactions. In this state the charges are spontaneously divided into solid and liquid component, and the former solid part aligns in a Wigner crystal manner while the latter moves among them like a pinball. We show that such charge ordered liquid is stable over a wide range of filling, $1/3<n<2/3$, and examine its filling dependent nature.Comment: 3 pages 3 figure

Multipole as ff-Electron Spin-Charge Density in Filled Skutterudites

It is shown that $f$-electron multipole is naturally defined as spin-charge one-electron density operator in the second-quantized form with the use of tensor operator on the analogy of multipole expansion of electromagnetic potential from charge distribution in electromagnetism. Due to this definition of multipole, it is possible to determine multipole state from a microscopic viewpoint on the basis of the standard linear response theory for multipole susceptibility. In order to discuss multipole properties of filled skutterudites, we analyze a seven-orbital impurity Anderson model by employing a numerical renormalization group method. We show our results on possible multipole states of filled skutterudite compounds.Comment: To appear in the Proceedings of International Conference on "New Quantum Phenomena in Skutterudite and Related Systems" (September 2007, Kobe, Japan

Effective Crystalline Electric Field Potential in a j-j Coupling Scheme

We propose an effective model on the basis of a $j$-$j$ coupling scheme to describe local $f$-electron states for realistic values of Coulomb interaction $U$ and spin-orbit coupling $\lambda$, for future development of microscopic theory of magnetism and superconductivity in $f^n$-electron systems, where $n$ is the number of local $f$ electrons. The effective model is systematically constructed by including the effect of a crystalline electric field (CEF) potential in the perturbation expansion in terms of $1/\lambda$. In this paper, we collect all the terms up to the first order of $1/\lambda$. Solving the effective model, we show the results of the CEF states for each case of $n$=2$\sim$5 with $O_{\rm h}$ symmetry in comparison with those of the Stevens Hamiltonian for the weak CEF. In particular, we carefully discuss the CEF energy levels in an intermediate coupling region with $\lambda/U$ in the order of 0.1 corresponding to actual $f$-electron materials between the $LS$ and $j$-$j$ coupling schemes. Note that the relevant energy scale of $U$ is the Hund's rule interaction. It is found that the CEF energy levels in the intermediate coupling region can be quantitatively reproduced by our modified $j$-$j$ coupling scheme, when we correctly take into account the corrections in the order of $1/\lambda$ in addition to the CEF terms and Coulomb interactions which remain in the limit of $\lambda$=$\infty$. As an application of the modified $j$-$j$ coupling scheme, we discuss the CEF energy levels of filled skutterudites with $T_{\rm h}$ symmetry.Comment: 12 pages, 7 figures. Typeset with jpsj2.cl

Enhanced Kondo Effect in an Electron System Dynamically Coupled with Local Optical Phonon

We discuss Kondo behavior of a conduction electron system coupled with local optical phonon by analyzing the Anderson-Holstein model with the use of a numerical renormalization group (NRG) method. There appear three typical regions due to the balance between Coulomb interaction $U_{\rm ee}$ and phonon-mediated attraction $U_{\rm ph}$. For $U_{\rm ee}>U_{\rm ph}$, we observe the standard Kondo effect concerning spin degree of freedom. Since the Coulomb interaction is effectively reduced as $U_{\rm ee}-U_{\rm ph}$, the Kondo temperature $T_{\rm K}$ is increased when $U_{\rm ph}$ is increased. On the other hand, for $U_{\rm ee}<U_{\rm ph}$, there occurs the Kondo effect concerning charge degree of freedom, since vacant and double occupied states play roles of pseudo-spins. Note that in this case, $T_{\rm K}$ is decreased with the increase of $U_{\rm ph}$. Namely, $T_{\rm K}$ should be maximized for $U_{\rm ee} \approx U_{\rm ph}$. Then, we analyze in detail the Kondo behavior at $U_{\rm ee}=U_{\rm ph}$, which is found to be explained by the polaron Anderson model with reduced hybridization of polaron and residual repulsive interaction among polarons. By comparing the NRG results of the polaron Anderson model with those of the original Anderson-Holstein model, we clarify the Kondo behavior in the competing region of $U_{\rm ee} \approx U_{\rm ph}$.Comment: 8 pages, 8 figure

Nonabelian Duality and Higgs Multiplets in Supersymmetric Grand Unified Theories

We consider strongly interacting supersymmetric gauge theories which break dynamically the GUT symmetry and produce the light Higgs doublets naturally. Two models we proposed in the previous articles are reanalyzed as two phases of one theory and are shown to have desired features. Furthermore, employing nonabelian duality proposed recently by Seiberg, we study the dual theory of the above one and show that the low-energy physics of the original and dual models are the same as expected. We note that the Higgs multiplets in the original model are regarded as composite states of the elementary hyperquarks in its dual theory. Theories with other hypercolors and similar matter contents are also analyzed in the same way.Comment: 16 pages, LaTeX, no figur

Dimensional tuning of electronic states under strong and frustrated interactions

We study a model of strongly interacting spinless fermions on an anisotropic triangular lattice. At half-filling and the limit of strong repulsive nearest-neighbor interactions, the fermions align in stripes and form an insulating state. When a particle is doped, it either follows a one-dimensional free motion along the stripes or fractionalizes perpendicular to the stripes. The two propagations yield a dimensional tuning of the electronic state. We study the stability of this phase and derive an effective model to describe the low-energy excitations. Spectral functions are presented which can be used to experimentally detect signatures of the charge excitations.Comment: 4pages 4figures included. to appear in Phys. Rev. Lett. vol. 10