Induced quantum numbers in the (2+1)-dimensional electron gas

A gas of electrons confined to a plane is examined in both the relativistic and nonrelativistic case. Using a (0+1)-dimensional effective theory, a remarkably simple method is proposed to calculate the spin density induced by an uniform magnetic background field. The physical properties of possible fluxon excitations are determined. It is found that while in the relativistic case they can be considered as half-fermions (semions) in that they carry half a fermion charge and half the spin of a fermion, in the nonrelativistic case they should be thought of as fermions, having the charge and spin of a fermion.Comment: 19 pages, REVTE

Self-Duality in Superconductor-Insulator Quantum Phase Transitions

It is argued that close to a Coulomb interacting quantum critical point, the interaction between two vortices in a disordered superconducting thin film separated by a distance $r$ changes from logarithmic in the mean-field region to $1/r$ in the region dominated by quantum critical fluctuations. This gives support to the charge-vortex duality picture of the observed reflection symmetry in the current-voltage characteristics on both sides of the transition.Comment: 4 pages, no figures, 2nd version: title (slightly) changed and text accordingl

Superconductor-insulator transition driven by local dephasing

We consider a system where localized bound electron pairs form an array of "Andreev"-like scattering centers and are coupled to a fermionic subsystem of uncorrelated electrons. By means of a path-integral approach, which describes the bound electron pairs within a coherent pseudospin representation, we derive and analyze the effective action for the collective phase modes which arise from the coupling between the two subsystems once the fermionic degrees of freedom are integrated out. This effective action has features of a quantum phase model in the presence of a Berry phase term and exhibits a coupling to a field which describes at the same time the fluctuations of density of the bound pairs and those of the amplitude of the fermion pairs. Due to the competition between the local and the hopping induced non-local phase dynamics it is possible, by tuning the exchange coupling or the density of the bound pairs, to trigger a transition from a phase ordered superconducting to a phase disordered insulating state. We discuss the different mechanisms which control this occurrence and the eventual destruction of phase coherence both in the weak and strong coupling limit.Comment: 16 pages, 5 figures, submitted to PRB (05-Feb04

Fractal Structure of Spin Clusters and Domain Walls in 2D Ising Model

The fractal structure of spin clusters and their boundaries in the critical two-dimensional (2D) Ising model is investigated numerically. The fractal dimensions of these geometrical objects are estimated by means of Monte Carlo simulations on relatively small lattices through standard finite-size scaling. The obtained results are in excellent agreement with theoretical predictions and partly provide significant improvements in precision over existing numerical estimates.Comment: 8 pages, 8 figures; v2: minor changes in text, various plots are put in one figur

Geometric invariant theory approach to the determination of ground states of D-wave condensates in isotropic space

A complete and rigorous determination of the possible ground states for D-wave pairing Bose condensates is presented, using a geometrical invariant theory approach to the problem. The order parameter is argued to be a vector, transforming according to a ten dimensional real representation of the group $G=${\bf O}$_3\otimes${\bf U}$_1\times$. We determine the equalities and inequalities defining the orbit space of this linear group and its symmetry strata, which are in a one-to-one correspondence with the possible distinct phases of the system. We find 15 allowed phases (besides the unbroken one), with different symmetries, that we thoroughly determine. The group-subgroup relations between bordering phases are pointed out. The perturbative sixth degree corrections to the minimum of a fourth degree polynomial $G$-invariant free energy, calculated by Mermin, are also determined.Comment: 27 revtex pages, 2 figures, use of texdraw; minor changes in the bibliography and in Table II

On the Ground State of Electron Gases at Negative Compressibility

Two- and three-dimensional electron gases with a uniform neutralizing background are studied at negative compressibility. Parametrized expressions for the dielectric function are used to access this strong-coupling regime, where the screened Coulomb potential becomes overall attractive for like charges. Closely examining these expressions reveals that the ground state with a periodic modulation of the charge density, albeit exponentially damped, replaces the homogeneous one at positive compressibility. The wavevector characterizing the new ground state depends on the density and is complex, having a positive imaginary part, as does the homogeneous ground state, and real part, as does the genuine charge density wave.Comment: 6 double-column pages, 2 figures. 2nd version is an extension of the 1st one, giving more detail

Multidimensional cut-off technique, odd-dimensional Epstein zeta functions and Casimir energy of massless scalar fields

Quantum fluctuations of massless scalar fields represented by quantum fluctuations of the quasiparticle vacuum in a zero-temperature dilute Bose-Einstein condensate may well provide the first experimental arena for measuring the Casimir force of a field other than the electromagnetic field. This would constitute a real Casimir force measurement - due to quantum fluctuations - in contrast to thermal fluctuation effects. We develop a multidimensional cut-off technique for calculating the Casimir energy of massless scalar fields in $d$-dimensional rectangular spaces with $q$ large dimensions and $d-q$ dimensions of length $L$ and generalize the technique to arbitrary lengths. We explicitly evaluate the multidimensional remainder and express it in a form that converges exponentially fast. Together with the compact analytical formulas we derive, the numerical results are exact and easy to obtain. Most importantly, we show that the division between analytical and remainder is not arbitrary but has a natural physical interpretation. The analytical part can be viewed as the sum of individual parallel plate energies and the remainder as an interaction energy. In a separate procedure, via results from number theory, we express some odd-dimensional homogeneous Epstein zeta functions as products of one-dimensional sums plus a tiny remainder and calculate from them the Casimir energy via zeta function regularization.Comment: 42 pages, 3 figures. v.2: typos corrected to match published versio

Acoustic Energy and Momentum in a Moving Medium

By exploiting the mathematical analogy between the propagation of sound in a non-homogeneous potential flow and the propagation of a scalar field in a background gravitational field, various wave ``energy'' and wave ``momentum'' conservation laws are established in a systematic manner. In particular the acoustic energy conservation law due to Blokhintsev appears as the result of the conservation of a mixed co- and contravariant energy-momentum tensor, while the exchange of relative energy between the wave and the mean flow mediated by the radiation stress tensor, first noted by Longuet-Higgins and Stewart in the context of ocean waves, appears as the covariant conservation of the doubly contravariant form of the same energy-momentum tensor.Comment: 25 Pages, Late

Nonperturbative XY-model approach to strong coupling superconductivity in two and three dimensions

For an electron gas with delta-function attraction we investigate the crossover from weak- to strong-coupling supercoductivity in two and three dimensions. We derive analytic expressions for the stiffness of phase fluctuations and set up effective XY-models which serve to determine nonperturbatively the temperature of phase decoherence where superconductivity breaks down. We find the transition temperature T_c as a monotonous function of the coupling strength and carrier density both in two and three dimensions, and give analytic formulas for the merging of the temperature of phase decoherence with the temperature of pair formation in the weak-coupling limit.Comment: Few typos corrected. Emails that were sent to the address [email protected] in June and July 1999 were lost in a computer crash, so if your comments were not answered please send them once mor

Pseudogap phase formation in the crossover from Bose-Einstein condensation to BCS superconductivity

A phase diagram for a 2D metal with variable carrier density has been derived. It consists of a normal phase, where the order parameter is absent; a so-called ``abnormal normal'' phase where this parameter is also absent but the mean number of composite bosons (bound pairs) exceeds the mean number of free fermions; a pseudogap phase where the absolute value of the order parameter gradually increases but its phase is a random value, and finally a superconducting (here Berezinskii-Kosterlitz-Thouless) phase. The characteristic transition temperatures between these phases are found. The chemical potential and paramagnetic susceptibility behavior as functions of the fermion density and the temperature are also studied. An attempt is made to qualitatively compare the resulting phase diagram with the features of underdoped high-$T_{c}$ superconducting compounds above their critical temperature.Comment: 26 pages, revtex, 5 EMTeX figures; more discussion and references added; to be published in JET