Fermi-Edge Singularity with Backscattering in the Luttinger-Liquid Model

We study the response of the interacting electron gas in one dimension on the local external potential. In the low frequency limit the power-law singularities are essentially modifyed by backscattering effects which, in the case of zero forward scattering, result in the universal critical exponent depending only on the Luttinger-liquid interactions. The results obtained may be used to describe singular responses of the 1D boson chains.Comment: 11 pages in LaTex, UBCTP-NP-93-00

Conductivity of thermally fluctuating superconductors in two dimensions

We review recent work on a continuum, classical theory of thermal fluctuations in two dimensional superconductors. A functional integral over a Ginzburg-Landau free energy describes the amplitude and phase fluctuations responsible for the crossover from Gaussian fluctuations of the superconducting order at high temperatures, to the vortex physics of the Kosterlitz-Thouless transition at lower temperatures. Results on the structure of this crossover are presented, including new results for corrections to the Aslamazov-Larkin fluctuation conductivity.Comment: 9 page

Comment on ``Hausdorff Dimension of Critical Fluctuations in Abelian Gauge Theories"

Hove, Mo, and Sudbo [Phys. Rev. Lett. 85, 2368 (2000)] derived a simple connection, $\eta + D_H = 2$, between the anomalous scaling dimension $\eta$ of the U(1) universality class order parameter and the Hausdorff dimension $D_H$ of critical loops in loop representations of U(1) models. We show that the above relation is wrong and establish a correct relation that contains a new critical exponent.Comment: In 1 revtex page with 1 figur

Theory of the spin bath

The quantum dynamics of mesoscopic or macroscopic systems is always complicated by their coupling to many "environmental" modes.At low T these environmental effects are dominated by localised modes, such as nuclear and paramagnetic spins, and defects (which also dominate the entropy and specific heat). This environment, at low energies, maps onto a "spin bath" model. This contrasts with "oscillator bath" models (originated by Feynman and Vernon) which describe {\it delocalised} environmental modes such as electrons, phonons, photons, magnons, etc. One cannot in general map a spin bath to an oscillator bath (or vice-versa); they constitute distinct "universality classes" of quantum environment. We show how the mapping to spin bath models is made, and then discuss several examples in detail, including moving particles, magnetic solitons, nanomagnets, and SQUIDs, coupled to nuclear and paramagnetic spin environments. We show how to average over spin bath modes, using an operator instanton technique, to find the system dynamics, and give analytic results for the correlation functions, under various conditions. We then describe the application of this theory to magnetic and superconducting systems.Particular attention is given to recent work on tunneling magnetic macromolecules, where the role of the nuclear spin bath in controlling the tunneling is very clear; we also discuss other magnetic systems in the quantum regime, and the influence of nuclear and paramagnetic spins on flux dynamics in SQUIDs.Comment: Invited article for Rep. Prog. Phys. to appear in April, 2000 (41 pages, latex, 13 figures. This is a strongly revised and extended version of previous preprint cond-mat/9511011

Worm Algorithm for Problems of Quantum and Classical Statistics

This is a chapter of the multi-author book "Understanding Quantum Phase Transitions," edited by Lincoln Carr and published by Taylor and Francis. In this chapter, we give a general introduction to the worm algorithm and present important results highlighting the power of the approachComment: 27 pages, 15 figures, chapter in a boo

Simulating the All-Order Strong Coupling Expansion I: Ising Model Demo

We investigate in some detail an alternative simulation strategy for lattice field theory based on the so-called worm algorithm introduced by Prokof'ev and Svistunov in 2001. It amounts to stochastically simulating the strong coupling expansion rather than the usual configuration sum. A detailed error analysis and an important generalization of the method are exemplified here in the simple Ising model. It allows for estimates of the two point function where in spite of exponential decay the signal to noise ratio does not degrade at large separation. Critical slowing down is practically absent. In the outlook some thoughts on the general applicability of the method are offered.Comment: 15 pages, 2 figures, refs. added, small language changes, to app. in Nucl. Phys. B[FS

Critical Point of a Weakly Interacting Two-Dimensional Bose Gas

We study the Berezinskii-Kosterlitz-Thouless transition in a weakly interacting 2D quantum Bose gas using the concept of universality and numerical simulations of the classical $|\psi|^4$-model on a lattice. The critical density and chemical potential are given by relations $n_c=(mT/2\pi \hbar^2) \ln(\xi \hbar^2/ mU)$ and $\mu_c=(mTU/\pi \hbar^2) \ln(\xi_{\mu} \hbar^2/ mU)$, where $T$ is the temperature, $m$ is the mass, and $U$ is the effective interaction. The dimensionless constant $\xi= 380 \pm 3$ is very large and thus any quantitative analysis of the experimental data crucially depends on its value. For $\xi_{\mu}$ our result is $\xi_{\mu} = 13.2 \pm 0.4$. We also report the study of the quasi-condensate correlations at the critical point.Comment: 4 pages (3 figures), Latex. Submitted to PR

Weakly interacting Bose gas in the vicinity of the critical point

We consider a three-dimensional weakly interacting Bose gas in the fluctuation region (and its vicinity) of the normal-superfluid phase transition point. We establish relations between basic thermodynamic functions: density, $n(T,\mu)$, superfluid density $n_s(T,\mu)$, and condensate density, $n_{\rm cnd} (T,\mu)$. Being universal for all weakly interacting $|\psi|^4$ systems, these relations are obtained from Monte Carlo simulations of the classical $|\psi|^4$ model on a lattice. Comparing with the mean-field results yields a quantitative estimate of the fluctuation region size. Away from the fluctuation region, on the superfluid side, all the data perfectly agree with the predictions of the quasicondensate mean field theory.--This demonstrates that the only effect of the leading above-the-mean-field corrections in the condensate based treatments is to replace the condensate density with the quasicondensate one in all local thermodynamic relations. Surprisingly, we find that a significant fraction of the density profile of a loosely trapped atomic gas might correspond to the fluctuation region.Comment: 14 pages, Latex, 8 figure