Anomalous criticality near semimetal-to-superfluid quantum phase transition in a two-dimensional Dirac cone model

We analyze the scaling behavior at and near a quantum critical point separating a semimetallic from a superfluid phase. To this end we compute the renormalization group flow for a model of attractively interacting electrons with a linear dispersion around a single Dirac point. We study both ground state and finite temperature properties. In two dimensions, the electrons and the order parameter fluctuations exhibit power-law scaling with anomalous scaling dimensions. The quasi-particle weight and the Fermi velocity vanish at the quantum critical point. The order parameter correlation length turns out to be infinite everywhere in the semimetallic ground state.Comment: 8 pages, 2 figures, typos correcte

Some Low-Temperature Properties of a Generalized Hubbard Model with Correlated Hopping

In the present paper we study some correlation effects in a generalized Hubbard model with correlated hopping within low-temperature region using a generalized mean-field approximation. It is shown that in a series of cases the model leads to consequences deviating essentially from those of the Hubbard model. We consider the possibility of applying the result to interpret the peculiarities of physical properties of systems with narrow energy bands.Comment: 2 pages, LaTex2e using Elsevier style, presented at LT22 Conference, Helsinki, August 199

Soft quantum vibrations of a PT-symmetric nonlinear ion chain

Theoretical Physic

Cosmological Neutrino Entanglement and Quantum Pressure

Context: The widespread view that cosmological neutrinos, even if massive, are well described since the decoupling redshift z~10^10 down to the present epoch by an almost perfectly collisionless fluid of classical point particles is re-examined. Aims: In view of the likely sub-eV rest mass of neutrinos, the main effects due to their fermionic nature are studied. Methods: By numerical means we calculate the accurate entropy, fugacity and pressure of cosmological neutrinos in the Universe expansion. By solving the Schroedinger equation we derive how and how fast semi-degenerate identical free fermions become entangled. Results: We find that for sub-eV neutrinos the exchange degeneracy has significantly increased during the relativistic to non-relativistic transition epoch at z~10^4-10^5. At all times neutrinos become entangled in less than 10^-6 s, much faster than any plausible decoherence time. The total pressure is increased by quantum effect from 5% at high redshifts to 68% at low redshifts with respect to a collisionless classical fluid. Conclusions: The quantum overpressure has no dynamical consequences in the homogeneous regime at high redshifts, but must be significant for neutrino clustering during the non-linear structure formation epoch at low redshifts.Comment: 11 pages, 7 figures, accepted version to Astronomy & Astrophysics (no change, correct wrong TeX rendering

Resistivity studies under hydrostatic pressure on a low-resistance variant of the quasi-2D organic superconductor kappa-(BEDT-TTF)2Cu[N(CN)2]Br: quest for intrinsic scattering contributions

Resistivity measurements have been performed on a low (LR)- and high (HR)-resistance variant of the kappa-(BEDT-TTF)_2Cu[N(CN)_2]Br superconductor. While the HR sample was synthesized following the standard procedure, the LR crystal is a result of a somewhat modified synthesis route. According to their residual resistivities and residual resistivity ratios, the LR crystal is of distinctly superior quality. He-gas pressure was used to study the effect of hydrostatic pressure on the different transport regimes for both variants. The main results of these comparative investigations are (i) a significant part of the inelastic-scattering contribution, which causes the anomalous rho(T) maximum in standard HR crystals around 90 K, is sample dependent, i.e. extrinsic in nature, (ii) the abrupt change in rho(T) at T* approx. 40 K from a strongly temperature-dependent behavior at T > T* to an only weakly T-dependent rho(T) at T < T* is unaffected by this scattering contribution and thus marks an independent property, most likely a second-order phase transition, (iii) both variants reveal a rho(T) proportional to AT^2 dependence at low temperatures, i.e. for T_c < T < T_0, although with strongly sample-dependent coefficients A and upper bounds for the T^2 behavior measured by T_0. The latter result is inconsistent with the T^2 dependence originating from coherent Fermi-liquid excitations.Comment: 8 pages, 6 figure

Anomalous scaling of fermions and order parameter fluctuations at quantum criticality

We analyze the quantum phase transition between a semimetal and a superfluid in a model of attractively interacting fermions with a linear dispersion. The quantum critical properties of this model cannot be treated by the Hertz-Millis approach since integrating out the fermions leads to a singular Landau-Ginzburg order parameter functional. We therefore derive and solve coupled renormalization group equations for the fermionic degrees of freedom and the bosonic order parameter fluctuations. In two spatial dimensions, fermions and bosons acquire anomalous scaling dimensions at the quantum critical point, associated with non-Fermi liquid behavior and non-Gaussian order parameter fluctuations.Comment: 8 pages, 9 figures, highlighted differences to Gross-Neveu model, updated version as publishe

Superconductivity from correlated hopping

We consider a chain described by a next-nearest-neighbor hopping combined with a nearest-neighbor spin flip. In two dimensions this three-body term arises from a mapping of the three-band Hubbard model for CuO$_2$ planes to a generalized $t-J$ model and for large O-O hopping favors resonance-valence-bond superconductivity of predominantly $d$-wave symmetry. Solving the ground state and low-energy excitations by analytical and numerical methods we find that the chain is a Luther-Emery liquid with correlation exponent $K_{\rho} = (2-n)^2/2$, where $n$ is the particle density.Comment: 10 pages, RevTeX 3.0 + 2 PostScript figs. Accepted for publication in Phys.Rev.

Magnetic Properties of the t-J Model in the Dynamical Mean-Field Theory

We present a theory for the spin correlation function of the t-J model in the framework of the dynamical mean-field theory. Using this mapping between the lattice and a local model we are able to obtain an intuitive expression for the non-local spin susceptibility, with the corresponding local correlation function as input. The latter is calculated by means of local Goldstone diagrams following closely the procedures developed and successfully applied for the (single impurity) Anderson model.We present a systematic study of the magnetic susceptibility and compare our results with those of a Hubbard model at large U. Similarities and differences are pointed out and the magnetic phase diagram of the t-J model is discussed.Comment: 28 pages LaTeX, postscript figures as compressed and uuencoded file included fil

Robustness of a local Fermi Liquid against Ferromagnetism and Phase Separation

We study the properties of Fermi Liquids with the microscopic constraint of a local self-energy. In this case the forward scattering sum-rule imposes strong limitations on the Fermi-Liquid parameters, which rule out any Pomeranchek instabilities. For both attractive and repulsive interactions, ferromagnetism and phase separation are suppressed. Superconductivity is possible in an s-wave channel only. We also study the approach to the metal-insulator transition, and find a Wilson ratio approaching 2. This ratio and other properties of Sr_{1-x}La_xTiO_3 are all consistent with the local Fermi Liquid scenario.Comment: 4 pages (twocolumn format), can compile with or without epsf.sty latex style file -- Postscript files: fig1.ps and fig2.p

Propagation of a hole on a Neel background

We analyze the motion of a single hole on a N\'eel background, neglecting spin fluctuations. Brinkman and Rice studied this problem on a cubic lattice, introducing the retraceable-path approximation for the hole Green's function, exact in a one-dimensional lattice. Metzner et al. showed that the approximationalso becomes exact in the infinite-dimensional limit. We introduce a new approach to this problem by resumming the Nagaoka expansion of the propagator in terms of non-retraceable skeleton-paths dressed by retraceable-path insertions. This resummation opens the way to an almost quantitative solution of the problemin all dimensions and, in particular sheds new light on the question of the position of the band-edges. We studied the motion of the hole on a double chain and a square lattice, for which deviations from the retraceable-path approximation are expected to be most pronounced. The density of states is mostly adequately accounted for by the retra\-ce\-able-path approximation. Our band-edge determination points towards an absence of band tails extending to the Nagaoka energy in the spectrums of the double chain and the square lattice. We also evaluated the spectral density and the self-energy, exhibiting k-dependence due to finite dimensionality. We find good agreement with recent numerical results obtained by Sorella et al. with the Lanczos spectra decoding method. The method we employ enables us to identify the hole paths which are responsible for the various features present in the density of states and the spectral density.Comment: 26 pages,Revte