A path integral ground state method

Sarsa, A.; Schmidt, Kevin; Magro, W. R.

doi:10.1063/1.481926

Cited by 210 publications

(217 citation statements)

References 27 publications

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“…The PIGS approach to the study of quantum systems consists in a systematic improvement of a trial wave function Ψ T by repeated application of the evolution operator in imaginary time, which eventually drives the system into the ground state, 15 according to the formula…”

Section: The Pigs Methodsmentioning

confidence: 99%

Condensate Fraction in Liquid 4He at Zero Temperature

Rota

Boronat

2011

J Low Temp Phys

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We present results of the one-body density matrix ρ 1 (r) and the condensate fraction n 0 of liquid 4 He calculated at zero temperature by means of the Path Integral Ground State Monte Carlo method. This technique allows to generate a highly accurate approximation for the ground state wave function Ψ 0 in a totally model-independent way, that depends only on the Hamiltonian of the system and on the symmetry properties of Ψ 0 . With this unbiased estimation of ρ 1 (r), we obtain precise results for the condensate fraction n 0 and the kinetic energy K of the system. The dependence of n 0 with the pressure shows an excellent agreement of our results with recent experimental measurements. Above the melting pressure, overpressurized liquid 4 He shows a small condensate fraction that has dropped to 0.8% at the highest pressure of p = 87 bar.

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Section: The Pigs Methodsmentioning

confidence: 99%

Condensate Fraction in Liquid 4He at Zero Temperature

Rota

Boronat

2011

J Low Temp Phys

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“…This algorithm can be generalized by generating trial moves for the paths according to any apriori probability distribution, and then accepting or rejecting them according to a Metropolis test done one the actual probability distribution for the paths, Eq. (5), 16 . The time correlation function of various observables which couple to external fields (such as, e.g., the electric dipole) are the Laplace transforms of spectral weight functions which, in some favorable cases, can be directly compared with experiments 7 .…”

Section: Reptation Quantum Monte Carlomentioning

confidence: 99%

Computer Simulation of Quantum Melting in Hydrogen Clusters

Baroni

Moroni²

2005

ChemPhysChem

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We introduce a new criterion-based on multipole dynamical correlations calculated within Reptation Quantum Monte Carlo-to discriminate between a melting vs. freezing behavior in quantum clusters. This criterion is applied to small clusters of para-hydrogen molecules (both pristine and doped with a CO cromophore), for cluster sizes around 12 molecules. This is a magic size at which para-hydrogen clusters display an icosahedral structure and a large stability. In spite of the similar geometric structure of CO@(pH2)12 and (pH2)13, the first system has a rigid, crystalline, behavior, while the second behaves more like a superfluid (or, possibly, a supersolid). 61.46.+w, 67.40.Yv, 36.40.Mr, 02.70.Ss Understanding the dynamics of quantum many-body systems is one of the major challenges presently set to theoretical and computational condensed-matter physicists. The combination of density-functional theory with molecular dynamics realized 20 years ago by Car and Parrinello 1 opened the way to the study of the dynamics of quantum driven classical systems (i.e. of atomic systems whose dynamics is essentially classical, but driven by quantum-mechanical forces). The development of density-functional perturbation theory has allowed for a systematic calculation of the low-lying quantum excited states of these same systems in the harmonic approximation 2 . Quantum Monte Carlo methods, on the other hand, have been very successful in describing the ground-state and finite-temperature properties of interacting bosons 3 and of lattice models of strongly interacting fermions 4 , and they promise a similar success in the study of chemical systems in the near future 5 . In spite of all these progresses, the ability to calculate in a reliable way the properties of the excited states of interacting quantum systems remains a largely unachieved goal. Recent advances in the quantum Monte Carlo methodology have partially changed this scenario, at least in what concerns systems whose ground-state wave-function is positive (i.e. bosons) and whose low-lying energy spectrum is dominated by few excited states, which is the typical situation for superfluids 6,7 . Thanks to these advances, it is now possible to calculate the low-lying excitation spectrum of clusters of up to a few tens 4 He atoms, possibly doped with some cromophore molecules which are experimentally used as spectroscopic probes of the dynamical and superfluid properties of the droplet. Molecular hydrogen, in its nuclear-spin realization called para-hydrogen (pH 2 , I = J = 0), is the only substance occurring in nature, other than 4 He, which can possibly exhibit the phenomenon of superfluidity at (not too) low temperature 8 . In spite of the lighter mass with respect to 4 He, the intermolecular potential is so much stronger that the estimated value of the λ-transition temperature (≈ 2 • K) is much lower than the observed triple-point temperature (13.96 • K). For this reason, much attention has been and is being paid to those confined geometries (such as clusters 9,10,11,12,1...

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“…These quantities can be computed in an unbiased fashion, i.e., the variational bias arising from the initial state (i.e., trial wave function (3)) can be essentially completely removed. 27 Results for e(N ) are shown in Fig. 1.…”

Section: Resultsmentioning

confidence: 99%

“…In this work, the method utilized is Path Integral ground state (PIGS), which is an extension to zero temperature of the standard, Path Integral Monte Carlo method. 26 27). Because this method is described in a number of publications, it will not be reviewed here.…”

Section: Methodsmentioning

confidence: 99%