Quantum vortex fluctuations in cuprate superconductors

We study the effects of quantum vortex fluctuations in two-dimensional superconductors using a dual theory of vortices, and investigate the relevance to underdoped cuprates where the superconductor-insulator transition (SIT) is possibly driven by quantum vortex proliferation. We find that a broad enough phase fluctuation regime may exist for experimental observation of the quantum vortex fluctuations near SIT in underdoped cuprates. We propose that this scenario can be tested via pair-tunneling experiments which measure the characteristic resonances in the zero-temperature pair-field susceptibility in the vortex-proliferated insulating phase.Comment: RevTex 5 pages, 2 eps figures; expanded; to appear in Phys. Rev.

Low frequency response of a collectively pinned vortex manifold

A low frequency dynamic response of a vortex manifold in type-II superconductor can be associated with thermally activated tunneling of large portions of the manifold between pairs of metastable states (two-level systems). We suggest that statistical properties of these states can be verified by using the same approach for the analysis of thermal fluctuations the behaviour of which is well known. We find the form of the response for the general case of vortex manifold with non-dispersive elastic moduli and for the case of thin superconducting film for which the compressibility modulus is always non-local.Comment: 8 pages, no figures, ReVTeX, the final version. Text strongly modified, all the results unchange

Pocket Monte Carlo algorithm for classical doped dimer models

We study the correlations of classical hardcore dimer models doped with monomers by Monte Carlo simulation. We introduce an efficient cluster algorithm, which is applicable in any dimension, for different lattices and arbitrary doping. We use this algorithm for the dimer model on the square lattice, where a finite density of monomers destroys the critical confinement of the two-monomer problem. The monomers form a two-component plasma located in its high-temperature phase, with the Coulomb interaction screened at finite densities. On the triangular lattice, a single pair of monomers is not confined. The monomer correlations are extremely short-ranged and hardly change with doping.Comment: 6 pages, REVTeX

On the existence of a Bose Metal at T=0

This paper aims to justify, at a microscopic level, the existence of a two-dimensional Bose metal, i.e. a metallic phase made out of Cooper pairs at T=0. To this end, we consider the physics of quantum phase fluctuations in (granular) superconductors in the absence of disorder and emphasise the role of two order parameters in the problem, viz. phase order and charge order. We focus on the 2-d Bose Hubbard model in the limit of very large fillings, i.e. a 2-d array of Josephson junctions. We find that the algebra of phase fluctuations is that of the Euclidean group $E_{2}$ in this limit, and show that the model is equivalent to two coupled XY models in (2+1)-d, one corresponding to the phase degrees of freedom, and the other the charge degrees of freedom. The Bose metal, then, is the phase in which both these degrees of freedom are disordered(as a result of quantum frustration). We analyse the model in terms of its topological excitations and suggest that there is a strong indication that this state represents a surface of critical points, akin to the gapless spin liquid states. We find a remarkable consistency of this scenario with certain low-T_c thin film experiments.Comment: 16 pages, 2 figure

Velocity-force characteristics of a driven interface in a disordered medium

Using a dynamic functional renormalization group treatment of driven elastic interfaces in a disordered medium, we investigate several aspects of the creep-type motion induced by external forces below the depinning threshold $f_c$: i) We show that in the experimentally important regime of forces slightly below $f_c$ the velocity obeys an Arrhenius-type law $v\sim\exp[-U(f)/T]$ with an effective energy barrier $U(f)\propto (f_{c}-f)$ vanishing linearly when f approaches the threshold $f_c$. ii) Thermal fluctuations soften the pinning landscape at high temperatures. Determining the corresponding velocity-force characteristics at low driving forces for internal dimensions d=1,2 (strings and interfaces) we find a particular non-Arrhenius type creep $v\sim \exp[-(f_c(T)/f)^{\mu}]$ involving the reduced threshold force $f_c(T)$ alone. For d=3 we obtain a similar v-f characteristic which is, however, non-universal and depends explicitly on the microscopic cutoff.Comment: 9 pages, RevTeX, 3 postscript figure

Velocity-force characteristics of an interface driven through a periodic potential

We study the creep dynamics of a two-dimensional interface driven through a periodic potential using dynamical renormalization group methods. We find that the nature of weak-drive transport depends qualitatively on whether the temperature $T$ is above or below the equilibrium roughening transition temperature $T_c$. Above $T_c$, the velocity-force characteristics is Ohmic, with linear mobility exhibiting a jump discontinuity across the transition. For $T \le T_c$, the transport is highly nonlinear, exhibiting an interesting crossover in temperature and weak external force $F$. For intermediate drive, $F>F_*$, we find near $T_c^{-}$ a power-law velocity-force characteristics $v(F)\sim F^\sigma$, with $\sigma-1\propto \tilde{t}$, and well-below $T_c$, $v(F)\sim e^{-(F_*/F)^{2\tilde{t}}}$, with $\tilde{t}=(1-T/T_c)$. In the limit of vanishing drive ($F\ll F_*$) the velocity-force characteristics crosses over to $v(F)\sim e^{-(F_0/F)}$, and is controlled by soliton nucleation.Comment: 18 pages, submitted to Phys. Rev.

Ground-state properties of the Rokhsar-Kivelson dimer model on the triangular lattice

We explicitly show that the Rokhsar-Kivelson dimer model on the triangular lattice is a liquid with topological order. Using the Pfaffian technique, we prove that the difference in local properties between the two topologically degenerate ground states on the cylinders and on the tori decreases exponentially with the system size. We compute the relevant correlation length and show that it equals the correlation length of the vison operator.Comment: 10 pages, 9 figure

Aging without disorder on long time scales

We study the Metropolis dynamics of a simple spin system without disorder, which exhibits glassy dynamics at low temperatures. We use an implementation of the algorithm of Bortz, Kalos and Lebowitz \cite{bortz}. This method turns out to be very efficient for the study of glassy systems, which get trapped in local minima on many different time scales. We find strong evidence of aging effects at low temperatures. We relate these effects to the distribution function of the trapping times of single configurations.Comment: 8 pages Revtex, 7 figures uuencoded (Revised version: the figures are now present

Geometric effects on T-breaking in p+ip and d+id superconductors

Superconducting order parameters that change phase around the Fermi surface modify Josephson tunneling behavior, as in the phase-sensitive measurements that confirmed $d$ order in the cuprates. This paper studies Josephson coupling when the individual grains break time-reversal symmetry; the specific cases considered are $p \pm ip$ and $d \pm id$, which may appear in Sr$_2$RuO$_4$ and Na$_x$CoO$_2 \cdot$(H$_2$O)$_y$ respectively. $T$-breaking order parameters lead to frustrating phases when not all grains have the same sign of time-reversal symmetry breaking, and the effects of these frustrating phases depend sensitively on geometry for 2D arrays of coupled grains. These systems can show perfect superconducting order with or without macroscopic $T$-breaking. The honeycomb lattice of superconducting grains has a superconducting phase with no spontaneous breaking of $T$ but instead power-law correlations. The superconducting transition in this case is driven by binding of fractional vortices, and the zero-temperature criticality realizes a generalization of Baxter's three-color model.Comment: 8 page

Theory of finite temperature crossovers near quantum critical points close to, or above, their upper-critical dimension

A systematic method for the computation of finite temperature ($T$) crossover functions near quantum critical points close to, or above, their upper-critical dimension is devised. We describe the physics of the various regions in the $T$ and critical tuning parameter ($t$) plane. The quantum critical point is at $T=0$, $t=0$, and in many cases there is a line of finite temperature transitions at $T = T_c (t)$, $t < 0$ with $T_c (0) = 0$. For the relativistic, $n$-component $\phi^4$ continuum quantum field theory (which describes lattice quantum rotor ($n \geq 2$) and transverse field Ising ($n=1$) models) the upper critical dimension is $d=3$, and for $d<3$, $\epsilon=3-d$ is the control parameter over the entire phase diagram. In the region $|T - T_c (t)| \ll T_c (t)$, we obtain an $\epsilon$ expansion for coupling constants which then are input as arguments of known {\em classical, tricritical,} crossover functions. In the high $T$ region of the continuum theory, an expansion in integer powers of $\sqrt{\epsilon}$, modulo powers of $\ln \epsilon$, holds for all thermodynamic observables, static correlators, and dynamic properties at all Matsubara frequencies; for the imaginary part of correlators at real frequencies ($\omega$), the perturbative $\sqrt{\epsilon}$ expansion describes quantum relaxation at $\hbar \omega \sim k_B T$ or larger, but fails for $\hbar \omega \sim \sqrt{\epsilon} k_B T$ or smaller. An important principle, underlying the whole calculation, is the analyticity of all observables as functions of $t$ at $t=0$, for $T>0$; indeed, analytic continuation in $t$ is used to obtain results in a portion of the phase diagram. Our method also applies to a large class of other quantum critical points and their associated continuum quantum field theories.Comment: 36 pages, 4 eps figure