Dynamic structure factor of superfluid He4 from quantum Monte Carlo: Maximum entropy revisited

Abstract

We use the Maximum Entropy Method (MaxEnt) to estimate the dynamic structure factor of superfluid 4 He at T = 1 K, by inverting imaginary-time density correlation functions computed by Quantum Monte Carlo (QMC) simulation. Our procedure consists of a Metropolis random walk in the space of all possible spectral images, sampled from a probability density which includes the entropic prior, in the context of the so-called "classic" MaxEnt. Comparison with recent work by other authors shows that, contrary to what is often stated, sharp features in the reconstructed image are not "washed out" by the entropic prior if the underlying QMC data have sufficient precision. Only spurious features that tend to appear in a straightforward χ 2 minimization are suppressed. arXiv:1808.08663v5 [cond-mat.stat-mech]

Density Response of the Warm Dense Electron Gas beyond Linear Response Theory: Excitation of Harmonics

“…with F (q, τ ) being the intermediate scattering function [45] evaluated at an imaginary time argument τ ∈ [0, β], see Refs. [58,60,[83][84][85][86][87][88][89] for different applications of this quantity. Finally, we mention the density of the perturbed electron gas in coordinate space, which, in LRT, is given by…”

Ab initio results for the plasmon dispersion and damping of the warm dense electron gas

“…For an overview on the results and comparisons with earlier models and simulations, see refs. [51,52].…”

“…This is known to be an ill‐posed problem that has occasionally been tackled using maximum entropy methods; see, for example, ref. [52] and references therein. Recently, it was found that a stochastic sampling of the LFCs G ( q , ω ) allows one to very well reconstruct the imaginary time density response function, and thus the dynamic structure factor, because additional exact constrains on the LFC makes the procedure very efficient and accurate.…”

Nonlinear density response from imaginary-time correlation functions: Ab initio path integral Monte Carlo simulations of the warm dense electron gas

“…First and foremost, our scheme gives one direct access to the nonlinear density response of all systems that can be simulated with the PIMC method. This includes such diverse applications as quantum-dipole system [18,19,97], ultracold atoms like 4 He [5,20], confined nano clusters [25][26][27], quantum crystals [11,12], and exotic supersolids [21,22]. Of particular interest is so-called warm dense matter [67,68], for which nonlinear effects have already been shown to play an important role [61,62] and, in addition, might constitute a promising new method of diagnostics [98].…”

“…Moreover, sophisticated sampling techniques [15,16] allow for the efficient simulation of up to N ∼ 10 4 bosons or boltzmannons (i.e., hypothetical distinguishable quantum particles). Consequently, the PIMC method has been successfully applied to a gamut of physical systems such as ultracold atoms [17][18][19][20], exotic supersolids [21][22][23], and confined nano-clusters [24][25][26][27][28]. While the PIMC simulation of quantum degenerate Fermi systems is rendered substantially more involved by the notorious fermion sign problem [29,30], the last decade has witnesses a spark of activity in this direction [31][32][33][34][35][36][37][38] as well, most notably in the context of socalled warm dense matter [39][40][41][42][43][44].…”