Competing density-wave orders in a one-dimensional hard-boson model

We describe the zero-temperature phase diagram of a model of bosons, occupying sites of a linear chain, which obey a hard-exclusion constraint: any two nearest-neighbor sites may have at most one boson. A special case of our model was recently proposed as a description of a ``tilted'' Mott insulator of atoms trapped in an optical lattice. Our quantum Hamiltonian is shown to generate the transfer matrix of Baxter's hard-square model. Aided by exact solutions of a number of special cases, and by numerical studies, we obtain a phase diagram containing states with long-range density-wave order with period 2 and period 3, and also a floating incommensurate phase. Critical theories for the various quantum phase transitions are presented. As a byproduct, we show how to compute the Luttinger parameter in integrable theories with hard-exclusion constraints.Comment: 16 page

Quantum Entanglement in Heisenberg Antiferromagnets

Entanglement sharing among pairs of spins in Heisenberg antiferromagnets is investigated using the concurrence measure. For a nondegenerate S=0 ground state, a simple formula relates the concurrence to the diagonal correlation function. The concurrence length is seen to be extremely short. A few finite clusters are studied numerically, to see the trend in higher dimensions. It is argued that nearest-neighbour concurrence is zero for triangular and Kagome lattices. The concurrences in the maximal-spin states are explicitly calculated, where the concurrence averaged over all pairs is larger than the S=0 states.Comment: 7 pages, 3 figure

A microscopic approach to critical phenomena at interfaces: an application to complete wetting in the Ising model

We study how the formalism of the Hierarchical Reference Theory (HRT) can be extended to inhomogeneous systems. HRT is a liquid state theory which implements the basic ideas of Wilson momentum shell renormalization group (RG) to microscopic Hamiltonians. In the case of homogeneous systems, HRT provides accurate results even in the critical region, where it reproduces scaling and non-classical critical exponents. We applied the HRT to study wetting critical phenomena in a planar geometry. Our formalism avoids the explicit definition of effective surface Hamiltonians but leads, close to the wetting transition, to the same renormalization group equation already studied by RG techiques. However, HRT also provides information on the non universal quantities because it does not require any preliminary coarse graining procedure. A simple approximation to the infinite HRT set of equations is discussed. The HRT evolution equation for the surface free energy is numerically integrated in a semi-infinite three-dimensional Ising model and the complete wetting phase transition is analyzed. A renormalization of the adsorption critical amplitude and of the wetting parameter is observed. Our results are compared to available Monte Carlo simulations.Comment: To be published in Phy. Rev.

Marginal Pinning of Quenched Random Polymers

An elastic string embedded in 3D space and subject to a short-range correlated random potential exhibits marginal pinning at high temperatures, with the pinning length $L_c(T)$ becoming exponentially sensitive to temperature. Using a functional renormalization group (FRG) approach we find $L_c(T) \propto \exp[(32/\pi)(T/T_{\rm dp})^3]$, with $T_{\rm dp}$ the depinning temperature. A slow decay of disorder correlations as it appears in the problem of flux line pinning in superconductors modifies this result, $\ln L_c(T)\propto T^{3/2}$.Comment: 4 pages, RevTeX, 1 figure inserte

Comment on "Observation of the conductivity coherence peak in superconducting Bi2Sr2CaCu2O8 single crystals"

Theoretical Physic

Correlation Functions for an Elastic String in a Random Potential: Instanton Approach

We develop an instanton technique for calculations of correlation functions characterizing statistical behavior of the elastic string in disordered media and apply the proposed approach to correlations of string free energies corresponding to different low-lying metastable positions. We find high-energy tails of correlation functions for the case of long-range disorder (the disorder correlation length well exceeds the characteristic distance between the sequential string positions) and short-range disorder with the correlation length much smaller then the characteristic string displacements. The former case refers to energy distributions and correlations on the distances below the Larkin correlation length, while the latter describes correlations on the large spatial scales relevant for the creep dynamics.Comment: 5 pages; 1 .eps figure include

Interface Hamiltonians and bulk critical behavior

FWN – Publicaties zonder aanstelling Universiteit Leide

Nonlocal Conductivity in the Vortex-Liquid Regime of a Two-Dimensional Superconductor

We have simulated the time-dependent Ginzburg-Landau equation with thermal fluctuations, to study the nonlocal dc conductivity of a superconducting film. Having examined points in the phase diagram at a wide range of temperatures and fields below the mean-field upper critical field, we find a portion of the vortex-liquid regime in which the nonlocal ohmic conductivity in real space is negative over a distance several times the spacing between vortices. The effect is suppressed when driven beyond linear response. Earlier work had predicted the existence of such a regime, due to the high viscosity of a strongly-correlated vortex liquid. This behavior is clearly distinguishable from the monotonic spatial fall-off of the conductivity in the higher temperature or field regimes approaching the normal state. The possibilities for experimental study of the nonlocal transport properties are discussed.Comment: 18 pages, revtex, 6 postscript figure

Comment on ``Phase ordering in chaotic map lattices with conserved dynamics''

Angelini, Pellicoro, and Stramaglia [Phys. Rev. E {\bf 60}, R5021 (1999), cond-mat/9907149] (APS) claim that the phase ordering of two-dimensional systems of sequentially-updated chaotic maps with conserved ``order parameter'' does not belong, for large regions of parameter space, to the expected universality class. We show here that these results are due to a slow crossover and that a careful treatment of the data yields normal dynamical scaling. Moreover, we construct better models, i.e. synchronously-updated coupled map lattices, which are exempt from these crossover effects, and allow for the first precise estimates of persistence exponents in this case.Comment: 3 pages, to be published in Phys. Rev.

Elastic Chain in a Random Potential: Simulation of the Displacement Function <(u(x)−u(0))2><(u(x)-u(0))^2> and Relaxation

We simulate the low temperature behaviour of an elastic chain in a random potential where the displacements $u(x)$ are confined to the {\it longitudinal} direction ($u(x)$ parallel to $x$) as in a one dimensional charge density wave--type problem. We calculate the displacement correlation function $g(x)=< (u(x)-u(0))^2>$ and the size dependent average square displacement $W(L)=$. We find that $g(x)\sim x^{2\eta}$ with $\eta\simeq3/4$ at short distances and $\eta\simeq3/5$ at intermediate distances. We cannot resolve the asymptotic long distance dependence of $g$ upon $x$. For the system sizes considered we find $g(L/2)\propto W\sim L^{2\chi}$ with $\chi\simeq2/3$. The exponent $\eta\simeq3/5$ is in agreement with the Random Manifold exponent obtained from replica calculations and the exponent $\chi\simeq2/3$ is consistent with an exact solution for the chain with {\it transverse} displacements ($u(x)$ perpendicular to $x$).The distribution of nearest distances between pinning wells and chain-particles is found to develop forbidden regions.Comment: 19 pages of LaTex, 6 postscript figures available on request, submitted to Journal of Physics A, MAJOR CHANGE