Variational theory of rotons in superfluid4He

Galli, D. E.; Reatto, L.; Vitiello, S. A.

doi:10.1007/bf00753386

Cited by 26 publications

(57 citation statements)

References 7 publications

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“…The intent of the present study is to show that this is indeed the case with values of τ manageable with present computational resources. Like for finite temperature PIMC, 7 also within PIGS the quantum system is mapped into a system of classical polymers, but in this case the polymers start and end on the initial wave function ψ T , 5,14,15 resulting in open linear polymers instead of the close ring ones of PIMC. 7 Each open polymer represents the full imaginary time path of a quantum particle that is sampled by means of the Metropolis algorithm.…”

Section: A the Pigs Methodsmentioning

confidence: 99%

“…In fact, the polymer configuration resulting after a permutation can be in principle reached with a combination of standard sampling moves, since the polymers are open. 14,15 This is not the case if ψ T is not Bose symmetric like the Gaussian wave function: permutation cycles among particles must be introduced in the sampling in order to get the exact ground state. For all ψ T we have implemented permutation sampling following Ref.…”

Section: A the Pigs Methodsmentioning

confidence: 99%

“…The properties of the SWF are so peculiar that the PIGS method that has a SWF as ψ T deserves an its own name and is dubbed SPIGS: Shadow Path Integral Ground State method. 14,15 In the picture of linear polymers, the presence of the shadow variables adds two extra variational links, one at each end of the polymer.…”

Section: Initial Wave Functionsmentioning

confidence: 99%

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Exact ground state Monte Carlo method for Bosons without importance sampling

Rossi

Nava

Reatto

et al. 2009

The Journal of Chemical Physics

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Generally "exact" Quantum Monte Carlo computations for the ground state of many Bosons make use of importance sampling. The importance sampling is based, either on a guiding function or on an initial variational wave function. Here we investigate the need of importance sampling in the case of Path Integral Ground State (PIGS) Monte Carlo. PIGS is based on a discrete imaginary time evolution of an initial wave function with a non zero overlap with the ground state, that gives rise to a discrete path which is sampled via a Metropolis like algorithm. In principle the exact ground state is reached in the limit of an infinite imaginary time evolution, but actual computations are based on finite time evolutions and the question is whether such computations give unbiased exact results. We have studied bulk liquid and solid 4 He with PIGS by considering as initial wave function a constant, i.e. the ground state of an ideal Bose gas. This implies that the evolution toward the ground state is driven only by the imaginary time propagator, i.e. there is no importance sampling. For both the phases we obtain results converging to those obtained by considering the best available variational wave function (the Shadow wave function) as initial wave function. Moreover we obtain the same results even by considering wave functions with the wrong correlations, for instance a wave function of a strongly localized Einstein crystal for the liquid phase. This convergence is true not only for diagonal properties such as the energy, the radial distribution function and the static structure factor, but also for off-diagonal ones, such as the one-body density matrix. This robustness of PIGS can be traced back to the fact that the chosen initial wave function acts only at the beginning of the path without affecting the imaginary time propagator. From this analysis we conclude that zero temperature PIGS calculations can be as unbiased as those of finite temperature Path Integral Monte Carlo. On the other hand, a judicious choice of the initial wave function greatly improves the rate of convergence to the exact results.

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Section: A the Pigs Methodsmentioning

confidence: 99%

Section: A the Pigs Methodsmentioning

confidence: 99%

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Exact ground state Monte Carlo method for Bosons without importance sampling

Rossi

Nava

Reatto

et al. 2009

The Journal of Chemical Physics

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“…As mentioned above exact QMC techniques are able to give access to estimations of S(q, ω) via exact calculations of dynamical correlation functions in imaginary time. The Path Integral Ground State (PIGS) method [27] and in particular the Shadow Path Integral Ground State (SPIGS) method [28,29] together with the Genetic Inversion via Falsification of Theories (GIFT) method [15] have been applied to bulk 4 He systems [15,17], to adsorbed 4 He systems [18] and even to a pure 2D 3 He system [30], (via a quite sophisticated novel strategy). Here we apply such approaches to address the calculation of dynamical properties of a pure 2D 4 He system at zero temperature.…”

Section: Introductionmentioning

confidence: 99%

Excitation spectrum in two-dimensional superfluid 4He

Arrigoni

Vitali

Galli

et al. 2013

Low Temperature Physics

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In this work we perform an ab-initio study of an ideal two-dimensional sample of 4He atoms, a model for 4He films adsorbed on several kinds of substrates. Starting from a realistic hamiltonian we face the microscopic study of the excitation phonon-roton spectrum of the system at zero temperature. Our approach relies on Path Integral Ground State Monte Carlo projection methods, allowing to evaluate exactly the dynamical density correlation functions in imaginary time, and this gives access to the dynamical structure factor of the system S(q,omega), containing information about the excitation spectrum E(q), resulting in sharp peaks in S(q,omega). The actual evaluation of S(q,omega) requires the inversion of the Laplace transform in ill-posed conditions, which we face via the Genetic Inversion via Falsification of Theories technique. We explore the full density range from the region of spinodal decomposition to the freezing density, i.e. 0.0321 A^-2 - 0.0658 A^-2. In particular we follow the density dependence of the excitation spectrum, focusing on the low wave--vector behavior of E(q), the roton dispersion, the strength of single quasi--particle peak, Z(q), and the static density response function, chi(q). As the density increases, the dispersion E(q) at low wave--vector changes from a super-linear (anomalous dispersion) trend to a sub-linear (normal dispersion) one, anticipating the crystallization of the system; at the same time the maxon-roton structure, which is barely visible at low density, becomes well developed at high densities and the roton wave vector has a strong density dependence. Connection is made with recent inelastic neutron scattering results from highly ordered silica nanopores partially filled with 4He.Comment: Accepted for publication: Special issue of FNT (Low Temp. Phys.) 75th anniversary of the discovery of superfluidit

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“…This is chiefly because the intensity in the single EE component of the observed dynamic structure factor, S(Q, ω), decreases rapidly with increasing Q beyond the roton and this peak "sits" on a sloping broad component of S(Q, ω) so that high instrument resolution is required to determine the peak position accurately. The excitations at Q values beyond the roton (BTR) are also much less well understood [6][7][8][9][10] and microscopic calculations of the EE energy [11][12][13] reproduce the observed EE energies less well for Q > 2.5Å −1 . In 1959, Pitaevskii proposed that the energy of the single EE, ω Q , had an upper limit.…”

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confidence: 99%

Excitations in superfluid ⁴ He beyond the roton

Glyde¹,

Gibbs²,

Stirling³

et al. 1998

Europhys. Lett.

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PACS. 67.40Db -Quantum statistical theory; ground state, elementary excitations. PACS. 61.12−q -Neutron diffraction and scattering.Abstract. -High-energy resolution inelastic neutron scattering data on excitations in superfluid and normal 4 He at SVP at wave vectors Q beyond the roton, 2.0 ≤ Q ≤ 4.0Å −1 , are presented. The narrow energy resolution of these measurements reveals that the energy of the elementary excitation comes up to twice the roton energy, 2∆, at Q = 2.8Å −1 and the energy remains constant at 2∆ between Q 3.0Å −1 and the end point of the dispersion curve at Q = 3.6Å −1 . The width of the peak is also unobservably small from Q = 2.8Å −1 out to the end point, W = 2Γ < 20 µeV.The energy and lifetime of the elementary phonon-roton excitations (EE) in superfluid 4 He are accurately known at low wave vector up to the roton wave vector, Q ∼ 1.92Å −1 at SVP [1][2][3][4][5]. However, the energy and lifetime of the EE for wave vectors beyond the roton, 2.5 < Q < 3.6Å −1 , are much less well determined. This is chiefly because the intensity in the single EE component of the observed dynamic structure factor, S(Q, ω), decreases rapidly with increasing Q beyond the roton and this peak "sits" on a sloping broad component of S(Q, ω) so that high instrument resolution is required to determine the peak position accurately. The excitations at Q values beyond the roton (BTR) are also much less well understood [6-10] and microscopic calculations of the EE energy [11][12][13] reproduce the observed EE energies less well for Q > 2.5Å −1 . In 1959, Pitaevskii proposed that the energy of the single EE, ω Q , had an upper limit. When the energy reached the energy of a pair of lower energy EE's, the single EE would decay into this pair. The single EE energy could not exceed this pair energy without decaying. The pair having the lowest energy which meets the conservation conditions for decay is two rotons. The ω Q should not exceed 2∆. In this picture, at the Q value where ω Q reaches 2∆, the single EE should also broaden. Earlier measurements [14][15][16][17] suggest that ω Q exceeds 2∆ for Q > 2.8Å −1 , particularly at higher pressure. The energies of Cowley and Woods for Q > 2.8Å −1 have been adopted as c EDP Sciences

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Variational theory of rotons in superfluid4He

Cited by 26 publications

References 7 publications

Exact ground state Monte Carlo method for Bosons without importance sampling

Exact ground state Monte Carlo method for Bosons without importance sampling

Excitation spectrum in two-dimensional superfluid 4He

Excitations in superfluid ⁴ He beyond the roton

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Variational theory of rotons in superfluid4He

Cited by 26 publications

References 7 publications

Exact ground state Monte Carlo method for Bosons without importance sampling

Exact ground state Monte Carlo method for Bosons without importance sampling

Excitation spectrum in two-dimensional superfluid 4He

Excitations in superfluid 4 He beyond the roton

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Excitations in superfluid ⁴ He beyond the roton