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

Universally diverging Grueneisen parameter and the magnetocaloric effect close to quantum critical points

At a generic quantum critical point, the thermal expansion $\alpha$ is more singular than the specific heat $c_p$. Consequently, the "Gr\"uneisen ratio'', \GE=\alpha/c_p, diverges. When scaling applies, \GE \sim T^{-1/(\nu z)} at the critical pressure $p=p_c$, providing a means to measure the scaling dimension of the most relevant operator that pressure couples to; in the alternative limit $T\to0$ and $p \ne p_c$, \GE \sim \frac{1}{p-p_c} with a prefactor that is, up to the molar volume, a simple {\it universal} combination of critical exponents. For a magnetic-field driven transition, similar relations hold for the magnetocaloric effect $(1/T)\partial T/\partial H|_S$. Finally, we determine the corrections to scaling in a class of metallic quantum critical points.Comment: 4 pages, 1 figure; general discussion on how the Grueneisen exponent measures the scaling dimension of the most relevant operator at any QCP is expande

Hamiltonian Formalism of the de-Sitter Invariant Special Relativity

Lagrangian of the Einstein's special relativity with universal parameter $c$ ($\mathcal{SR}_c$) is invariant under Poincar\'e transformation which preserves Lorentz metric $\eta_{\mu\nu}$. The $\mathcal{SR}_c$ has been extended to be one which is invariant under de Sitter transformation that preserves so called Beltrami metric $B_{\mu\nu}$. There are two universal parameters $c$ and $R$ in this Special Relativity (denote it as $\mathcal{SR}_{cR}$). The Lagrangian-Hamiltonian formulism of $\mathcal{SR}_{cR}$ is formulated in this paper. The canonic energy, canonic momenta, and 10 Noether charges corresponding to the space-time's de Sitter symmetry are derived. The canonical quantization of the mechanics for $\mathcal{SR}_{cR}$-free particle is performed. The physics related to it is discussed.Comment: 24 pages, no figur

How do Fermi liquids get heavy and die?

We discuss non-Fermi liquid and quantum critical behavior in heavy fermion materials, focussing on the mechanism by which the electron mass appears to diverge at the quantum critical point. We ask whether the basic mechanism for the transformation involves electron diffraction off a quantum critical spin density wave, or whether a break-down in the composite nature of the heavy electron takes place at the quantum critical point. We show that the Hall constant changes continously in the first scenario, but may ``jump'' discontinuously at a quantum critical point where the composite character of the electron quasiparticles changes.Comment: Revised version with many new references added. To appear as a topical review in Journal of Physics: Condensed Matter Physics. Two column version http://www.physics.rutgers.edu/~coleman/online/questions.ps.g

Break up of heavy fermions at an antiferromagnetic instability

We present results of high-resolution, low-temperature measurements of the Hall coefficient, thermopower, and specific heat on stoichiometric YbRh2Si2. They support earlier conclusions of an electronic (Kondo-breakdown) quantum critical point concurring with a field induced antiferromagnetic one. We also discuss the detachment of the two instabilities under chemical pressure. Volume compression/expansion (via substituting Rh by Co/Ir) results in a stabilization/weakening of magnetic order. Moderate Ir substitution leads to a non-Fermi-liquid phase, in which the magnetic moments are neither ordered nor screened by the Kondo effect. The so-derived zero-temperature global phase diagram promises future studies to explore the nature of the Kondo breakdown quantum critical point without any interfering magnetism.Comment: minor changes, accepted for publication in JPS

Field-driven femtosecond magnetization dynamics induced by ultrastrong coupling to THz transients

Controlling ultrafast magnetization dynamics by a femtosecond laser is attracting interest both in fundamental science and industry because of the potential to achieve magnetic domain switching at ever advanced speed. Here we report experiments illustrating the ultrastrong and fully coherent light-matter coupling of a high-field single-cycle THz transient to the magnetization vector in a ferromagnetic thin film. We could visualize magnetization dynamics which occur on a timescale of the THz laser cycle and two orders of magnitude faster than the natural precession response of electrons to an external magnetic field, given by the Larmor frequency. We show that for one particular scattering geometry the strong coherent optical coupling can be described within the framework of a renormalized Landau Lifshitz equation. In addition to fundamentally new insights to ultrafast magnetization dynamics the coherent interaction allows for retrieving the complex time-frequency magnetic properties and points out new opportunities in data storage technology towards significantly higher storage speed.Comment: 25 page

Type Ia Supernova Explosion Models

Because calibrated light curves of Type Ia supernovae have become a major tool to determine the local expansion rate of the Universe and also its geometrical structure, considerable attention has been given to models of these events over the past couple of years. There are good reasons to believe that perhaps most Type Ia supernovae are the explosions of white dwarfs that have approached the Chandrasekhar mass, M_ch ~ 1.39 M_sun, and are disrupted by thermonuclear fusion of carbon and oxygen. However, the mechanism whereby such accreting carbon-oxygen white dwarfs explode continues to be uncertain. Recent progress in modeling Type Ia supernovae as well as several of the still open questions are addressed in this review. Although the main emphasis will be on studies of the explosion mechanism itself and on the related physical processes, including the physics of turbulent nuclear combustion in degenerate stars, we also discuss observational constraints.Comment: 38 pages, 4 figures, Annual Review of Astronomy and Astrophysics, in pres

The break up of heavy electrons at a quantum critical point

The point at absolute zero where matter becomes unstable to new forms of order is called a quantum critical point (QCP). The quantum fluctuations between order and disorder that develop at this point induce profound transformations in the finite temperature electronic properties of the material. Magnetic fields are ideal for tuning a material as close as possible to a QCP, where the most intense effects of criticality can be studied. A previous study on theheavy-electron material $YbRh_2Si_2$ found that near a field-induced quantum critical point electrons move ever more slowly and scatter off one-another with ever increasing probability, as indicated by a divergence to infinity of the electron effective mass and cross-section. These studies could not shed light on whether these properties were an artifact of the applied field, or a more general feature of field-free QCPs. Here we report that when Germanium-doped $YbRh_2Si_2$ is tuned away from a chemically induced quantum critical point by magnetic fields there is a universal behavior in the temperature dependence of the specific heat and resistivity: the characteristic kinetic energy of electrons is directly proportional to the strength of the applied field. We infer that all ballistic motion of electrons vanishes at a QCP, forming a new class of conductor in which individual electrons decay into collective current carrying motions of the electron fluid.Comment: Pdf files of article available at http://www.physics.rutgers.edu/~coleman/online/breakup.pdf, pdf file of news and views article available at http://www.physics.rutgers.edu/~coleman/online/nvbreakup.pd

Spin-dependent transport in a Luttinger liquid

We develop a detailed theory for spin transport in a one-dimensional quantum wire described by Luttinger liquid theory. A hydrodynamic description for the quantum wire is supplemented by boundary conditions taking into account the exchange coupling between the magnetization of ferromagnetic reservoirs and the boundary magnetization in the wire. Spin-charge separation is shown to imply drastic and qualitative consequences for spin-dependent transport. In particular, the spin accumulation effect is quenched except for fine-tuned parameter regimes. We propose several feasible setups involving an external magnetic field to detect this phenomenon in transport experiments on single-wall carbon nanotubes. In addition, electron-electron backscattering processes, which do not have an important effect on thermodynamic properties or charge transport, are shown to modify spin-dependent transport through long quantum wires in a crucial way.Comment: 23 pages, 4 figure

Adaptation of the Landau-Migdal Quasiparticle Pattern to Strongly Correlated Fermi Systems

A quasiparticle pattern advanced in Landau's first article on Fermi liquid theory is adapted to elucidate the properties of a class of strongly correlated Fermi systems characterized by a Lifshitz phase diagram featuring a quantum critical point (QCP) where the density of states diverges. The necessary condition for stability of the Landau Fermi Liquid state is shown to break down in such systems, triggering a cascade of topological phase transitions that lead, without symmetry violation, to states with multi-connected Fermi surfaces. The end point of this evolution is found to be an exceptional state whose spectrum of single-particle excitations exhibits a completely flat portion at zero temperature. Analysis of the evolution of the temperature dependence of the single-particle spectrum yields results that provide a natural explanation of classical behavior of this class of Fermi systems in the QCP region.Comment: 26 pages, 14 figures. Dedicated to 100th anniversary of A.B.Migdal birthda