Non-Fermi Liquids in the Extended Hubbard Model

I summarize recent work on non-Fermi liquids within certain generalized Anderson impurity model as well as in the large dimensionality ($D$) limit of the two-band extended Hubbard model. The competition between local charge and spin fluctuations leads either to a Fermi liquid with renormalized quasiparticle excitations, or to non-Fermi liquids with spin-charge separation. These results provide new insights into the phenomenological similarities and differences between different correlated metals. While presenting these results, I outline a general strategy of local approach to non-Fermi liquids in correlated electron systems.Comment: 30 pages, REVTEX, 14 figures included. To appear in ``Non Fermi Liquid Physics'', J. Phys: Cond. Matt. (1997

Effect of conduction electron interactions on Anderson impurities

The effect of conduction electron interactions for an Anderson impurity is investigated in one dimension using a scaling approach. The flow diagrams are obtained by solving the renormalization group equations numerically. It is found that the Anderson impurity case is different from its counterpart -- the Kondo impurity case even in the local moment region. The Kondo temperature for an Anderson impurity shows nonmonotonous behavior, increasing for weak interactions but decreasing for strong interactions. The implication of the study to other related impurity models is also discussed.Comment: 10 pages, revtex, 4 figures (the postscript file is included), to appear in Phys. Rev. B (Rapid Commun.

Fermi-surface collapse and dynamical scaling near a quantum critical point

Quantum criticality arises when a macroscopic phase of matter undergoes a continuous transformation at zero temperature. While the collective fluctuations at quantum-critical points are being increasingly recognized as playing an important role in a wide range of quantum materials, the nature of the underlying quantum-critical excitations remains poorly understood. Here we report in-depth measurements of the Hall effect in the heavy-fermion metal YbRh2Si2, a prototypical system for quantum criticality. We isolate a rapid crossover of the isothermal Hall coefficient clearly connected to the quantum-critical point from a smooth background contribution; the latter exists away from the quantum-critical point and is detectable through our studies only over a wide range of magnetic field. Importantly, the width of the critical crossover is proportional to temperature, which violates the predictions of conventional theory and is instead consistent with an energy over temperature, E/T, scaling of the quantum-critical single-electron fluctuation spectrum. Our results provide evidence that the quantum-dynamical scaling and a critical Kondo breakdown simultaneously operate in the same material. Correspondingly, we infer that macroscopic scale-invariant fluctuations emerge from the microscopic many-body excitations associated with a collapsing Fermi-surface. This insight is expected to be relevant to the unconventional finite-temperature behavior in a broad range of strongly correlated quantum systems.Comment: 5 pages, plus supporting materia

Electrical resistivity ofYb(Rh1-xCox)2Si2 single crystals at low temperatures

We report low-temperature measurements of the electrical resistivity of Yb(Rh1-xCox)2Si2 single crystals with 0 <= x <= 0.12. The isoelectronic substitution of Co on the Rh site leads to a decrease of the unit cell volume which stabilizes the antiferromagnetism. Consequently, the antiferromagnetic transition temperature increases upon Co substitution. For x = 0.07 Co content a subsequent low-temperature transition is observed in agreement with susceptibility measurements and results on YbRh2Si2 under hydrostatic pressure. Above the Neel transition the resistivity follows a non-Fermi liquid behavior similar to that of YbRh2Si2.Comment: 4 pages, submitted to SCES0

Kosterlitz-Thouless Transition and Short Range Spatial Correlations in an Extended Hubbard Model

We study the competition between intersite and local correlations in a spinless two-band extended Hubbard model by taking an alternative limit of infinite dimensions. We find that the intersite density fluctuations suppress the charge Kondo energy scale and lead to a Fermi liquid to non-Fermi liquid transition for repulsive on-site density-density interactions. In the absence of intersite interactions, this transition reduces to the known Kosterlitz-Thouless transition. We show that a new line of non-Fermi liquid fixed points replace those of the zero intersite interaction problem.Comment: 11 pages, 2 figure

Andreev Reflection and Spin Injection into s−s- and d−d-wave Superconductors

We study the effect of spin injection into $s-$ and $d-$wave superconductors, with an emphasis on the interplay between boundary and bulk spin transport properties. The quantities of interest include the amount of non-equilibrium magnetization ($m$), as well as the induced spin-dependent current ($I_s$) and boundary voltage ($V_s$). In general, the Andreev reflection makes each of the three quantities depend on a different combination of the boundary and bulk contributions. The situation simplifies either for half-metallic ferromagnets or in the strong barrier limit, where both $V_s$ and $m$ depend solely on the bulk spin transport/relaxation properties. The implications of our results for the on-going spin injection experiments in high $T_c$ cuprates are discussed.Comment: 4 pages, REVTEX, 1 figure included; typos correcte

Correlation Induced Insulator to Metal Transitions

We study a spinless two-band model at half-filling in the limit of infinite dimensions. The ground state of this model in the non-interacting limit is a band-insulator. We identify transitions to a metal and to a charge-Mott insulator, using a combination of analytical, Quantum Monte Carlo, and zero temperature recursion methods. The metallic phase is a non-Fermi liquid state with algebraic local correlation functions with universal exponents over a range of parameters.Comment: 12 pages, REVTE

Bubble concentration on spheres for supercritical elliptic problems

We consider the supercritical Lane-Emden problem (P_\eps)\qquad -\Delta v= |v|^{p_\eps-1} v \ \hbox{in}\ \mathcal{A} ,\quad u=0\ \hbox{on}\ \partial\mathcal{A} where $\mathcal A$ is an annulus in \rr^{2m}, $m\ge2$ and p_\eps={(m+1)+2\over(m+1)-2}-\eps, \eps>0. We prove the existence of positive and sign changing solutions of (P_\eps) concentrating and blowing-up, as \eps\to0, on $(m-1)-$dimensional spheres. Using a reduction method (see Ruf-Srikanth (2010) J. Eur. Math. Soc. and Pacella-Srikanth (2012) arXiv:1210.0782)we transform problem (P_\eps) into a nonhomogeneous problem in an annulus \mathcal D\subset \rr^{m+1} which can be solved by a Ljapunov-Schmidt finite dimensional reduction

Fixed-point elimination in the intuitionistic propositional calculus

It is a consequence of existing literature that least and greatest fixed-points of monotone polynomials on Heyting algebras-that is, the algebraic models of the Intuitionistic Propositional Calculus-always exist, even when these algebras are not complete as lattices. The reason is that these extremal fixed-points are definable by formulas of the IPC. Consequently, the $\mu$-calculus based on intuitionistic logic is trivial, every $\mu$-formula being equivalent to a fixed-point free formula. We give in this paper an axiomatization of least and greatest fixed-points of formulas, and an algorithm to compute a fixed-point free formula equivalent to a given $\mu$-formula. The axiomatization of the greatest fixed-point is simple. The axiomatization of the least fixed-point is more complex, in particular every monotone formula converges to its least fixed-point by Kleene's iteration in a finite number of steps, but there is no uniform upper bound on the number of iterations. We extract, out of the algorithm, upper bounds for such n, depending on the size of the formula. For some formulas, we show that these upper bounds are polynomial and optimal