A misprint was found in the last digit of the parameter C 0 of Table II. The correct value is C 0 0:057 238 4. Moreover, to reobtain exactly Fig. 3, one has to use G 0 0:339 97 (not G 0 0:34 as originally printed). The use of the misprinted values of C 0 and G 0 which appear in the original version of Table II does not affect the results for r s & 30; it does, instead, shift the Wigner crystallization to slightly larger r s .Finally, the text following Eq.(3) has two rather obvious misprints: the factors of 2 and 24 instead of 1=2 and 1=24 in the definitions of 1 and 2 . This is completely harmless: all results and equations of the Letter are based on the correct definition, not on the misprinted one.
We introduce a new stochastic method for calculating ground-state properties of quantum systems. Segments of a Langevin random walk guided by a trial wave function are subject to a Metropolis rejection test performed on the time integral of the local energy. The algorithm -which is as simple as variational Monte Carlo -for bosons provides exact expectation values of local observables, as well as their static and dynamic (in imaginary time) response functions, without mixed-estimate nor population-control biases. Our method is demonstrated with a few case applications to 4 He.[S0031-9007(99)09325-4] PACS numbers: 05.10.Gg, 05.40.Fb, 05.60.Gg The analogies existing between the classical diffusion equation and the quantum imaginary-time Schrödinger equation constitute the basis of a simulation methodknown as diffusion Monte Carlo (DMC)-which has been successfully applied to the study of interacting bosons and fermions at zero temperature [1,2]. The DMC crucially relies on importance sampling, i.e., on letting the diffusing walkers be guided by our prior knowledge of some approximate wave function, F 0 , for the system under study. The resulting stochastic process consists of a (biased) diffusion term plus a branching term which determine the variation of the local number of random walkers. Sampling the asymptotic distribution of the random walk allows one to calculate the ground-state energy exactly within statistical noise (at least for bosons). However, the calculation of observables which do not commute with the Hamiltonian requires the so-called mixed estimate [2]-a procedure which is biased by the trial function. One can remove this bias and obtain information on imaginary-time correlations by the forward walking technique [3] which, however, substantially increases the statistical noise. The control of the walker population introduces a further systematic error [1,2] whose elimination [2] leads to additional fluctuations.In this paper we propose a new method, named reptation quantum Monte Carlo (RQMC) [4], which avoids the above difficulties by exploiting the dynamical properties of the classical diffusion process-rather than retaining the asymptotic distribution alone-and mapping them onto the (imaginary-time) dynamical properties of the quantum system of interest. In the following we first discuss the formalism starting from classical diffusion as described by the Langevin equation; we then outline an algorithm suitable for practical implementations, and, finally, we present results for superfluid 4 He which are meant to be representative of the potential of the method.The time-discretized Langevin equation, x͑t 1 e͒ x͑t͒ 1 f͑ ͑ ͑x͑t͒͒ ͒ ͒e 1 j͑t͒ ,describes the motion in configuration space under a deterministic force f͑x͒ and a white noise j [͗j͑t͒͘ 0, ͗j͑t͒j͑t 0 ͒͘ 2ed tt 0 ]. For notational simplicity, in Eq.(1) and in the following, we consider a onedimensional system, the generalization to many dimensions being straightforward. The process described by Eq. (1) is readily simulated by a pseudorandom...
We have evaluated the density-density static response of a many-body system by calculating with the quantum Monte Carlo method the energy and density change caused by an external potential. Our results for the linear response function of liquid ^He at zero pressure and temperature are in excellent agreement with the available experimental data. The results for the response function of 2D electrons also at zero temperature, obtained within the fixed-node approximation, constitute the most accurate information available to date for this system. PACS numbers: 05.30.-d, 02.50.-l-sThe quantum Monte Carlo method (QMC) provides a systematic route to the calculation of exact properties of many-body systems [1]. For bosons, in particular, stable algorithms exist that yield virtually exact results [2,3]. This is not the case with fermions, which suffer from the so-called sign problem. However, very accurate results have been obtained for a number of systems, ranging from the homogeneous electron fluid [4,5], to light molecules [6], and to solid hydrogen [7], using the fixednode approximation. The vast majority of calculations to date have been for equilibrium properties such as energy, one-particle-orbital occupation numbers, and static correlation functions. Calculations of time-dependent correlation functions and of the related response functions [8] have been lacking for continuum systems. With the exception of some recent progress [9] for lattice models, the same lack of results holds for the static response functions which are properties of the many-body system that, apart from their intrinsic interest, are of importance to density functional developments beyond LDA [10] and crucial to the recently developed theory of quantum freezing [11].We show that the static density-density response function is directly calculable by QMC with little increase in technical complexity as compared with other properties. We directly use the definition of static response function, rather than evaluate it in terms of the time-dependent correlations, via the fluctuation-dissipation theorem [8]. We apply a static external potential, '^ext(r) = 2t;qCOs(q-r),which induces a modulation of the density with respect to its mean value, no. Such a modulation contains periodic components at all wave vectors that are nonvanishing integer multiples of q. In particular, one finds a modulation with wave vector q, ni(r) = 2nqCos(q • r), wherespace. Similarly the ground-state energy (per particle) can be expanded in even powers of v^:only contains odd powers of t^q. Here X(Q) denotes the static density-density linear response function in FourierThe coeSicients C3 and C4 in the above equations are determined by the cubic response function [12]. QMC allows the direct evaluation of both nq and Ey^ for given q and fq. We perform simulations at a few coupling strengths v^ and then extract X{Q) ^S well as the higherorder response functions from the calculated nq or Ey, by fitting in powers of t'q. As an illustration, we have chosen to study superfluid "^He an...
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.