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

Supersolids: what and where are they ?

The ongoing experimental and theoretical effort aimed at understanding non-classical rotational inertia in solid helium, has sparked renewed interest in the supersolid phase of matter, its microscopic origin and character, and its experimental detection. The purpose of this colloquium is a) to provide a general theoretical framework for the phenomenon of supersolidity and b) to review some of the experimental evidence for solid Helium-four, and discuss its possible interpretation in terms of physical effects underlain by extended defects (such as dislocations). We provide quantitative support to our theoretical scenarios by means of first principle numerical simulations. We also discuss alternate avenues for the observation of the supersolid phase, not involving helium but rather assemblies of ultracold atoms.Comment: 20 pages, 7 figures, accepted for publication as a Colloquium in the Review of Modern Physic

Comment on "Phase Diagram of a Disordered Boson Hubbard Model in Two Dimensions"

We prove that previous claims of observing a direct superfluid-Mott insulator transition in the disordered J-current model are in error because numerical simulations were done for too small system sizes and the authors ignored the rigorous theorem.Comment: 1 page, Latex, 1 figur

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

Two-Dimensional Weakly Interacting Bose Gas in the Fluctuation Region

We study the crossover between the mean-field and critical behavior of the two-dimensional Bose gas throughout the fluctuation region of the Berezinskii--Kosterlitz--Thouless phase transition point. We argue that this crossover is described by universal (for all weakly interacting |psi|^4 models) relations between thermodynamic parameters of the system, including superfluid and quasi-condensate densities. We establish these relations with high-precision Monte Carlo simulations of the classical |psi|^4 model on a lattice, and check their asymptotic forms against analytic expressions derived on the basis of the mean-field theory.Comment: Revtex, 8 pages, 8 figures; submitted to Phys. Rev. A; extended discussion of effective interaction and of a trapped gas; corrected typo in Eq. (32