8,880 research outputs found
Bose Einstein Condensation of incommensurate solid 4He
It is pointed out that simulation computation of energy performed so far
cannot be used to decide if the ground state of solid 4He has the number of
lattice sites equal to the number of atoms (commensurate state) or if it is
different (incommensurate state). The best variational wave function, a shadow
wave function, gives an incommensurate state but the equilibrium concentration
of vacancies remains to be determined. In order to investigate the presence of
a supersolid phase we have computed the one--body density matrix in solid 4He
for the incommensurate state by means of the exact Shadow Path Integral Ground
State projector method. We find a vacancy induced Bose Einstein condensation of
about 0.23 atoms per vacancy at a pressure of 54 bar. This means that bulk
solid 4He is supersolid at low enough temperature if the exact ground state is
incommensurate.Comment: 5 pages, 2 figure
Dynamic structure factor for 3He in two-dimensions
Recent neutron scattering experiments on 3He films have observed a zero-sound
mode, its dispersion relation and its merging with -and possibly emerging from-
the particle-hole continuum. Here we address the study of the excitations in
the system via quantum Monte Carlo methods: we suggest a practical scheme to
calculate imaginary time correlation functions for moderate-size fermionic
systems. Combined with an efficient method for analytic continuation, this
scheme affords an extremely convincing description of the experimental
findings.Comment: 5 pages, 5 figure
Implementation of the Linear Method for the optimization of Jastrow-Feenberg and Backflow Correlations
We present a fully detailed and highly performing implementation of the
Linear Method [J. Toulouse and C. J. Umrigar (2007)] to optimize
Jastrow-Feenberg and Backflow Correlations in many-body wave-functions, which
are widely used in condensed matter physics. We show that it is possible to
implement such optimization scheme performing analytical derivatives of the
wave-function with respect to the variational parameters achieving the best
possible complexity O(N^3) in the number of particles N.Comment: submitted to the Comp. Phys. Com
Imaginary Time Correlations and the phaseless Auxiliary Field Quantum Monte Carlo
The phaseless Auxiliary Field Quantum Monte Carlo method provides a well
established approximation scheme for accurate calculations of ground state
energies of many-fermions systems. Here we apply the method to the calculation
of imaginary time correlation functions. We give a detailed description of the
technique and we test the quality of the results for static and dynamic
properties against exact values for small systems.Comment: 13 pages, 6 figures; submitted to J. Chem. Phy
Bounds for the Superfluid Fraction from Exact Quantum Monte Carlo Local Densities
For solid 4He and solid p-H2, using the flow-energy-minimizing one-body phase
function and exact T=0 K Monte Carlo calculations of the local density, we have
calculated the phase function, the velocity profile and upper bounds for the
superfluid fraction f_s. At the melting pressure for solid 4He we find that f_s
< 0.20-0.21, about ten times what is observed. This strongly indicates that the
theory for the calculation of these upper bounds needs substantial
improvements.Comment: to be published in Phys. Rev. B (Brief Reports
Exact ground state Monte Carlo method for Bosons without importance sampling
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 4He 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. From this analysis we
conclude that zero temperature PIGS calculations can be as unbiased as those of
finite temperature Path Integral Monte Carlo.Comment: 11 pages, 10 figure
Quantum dislocations: the fate of multiple vacancies in two dimensional solid 4He
Defects are believed to play a fundamental role in the supersolid state of
4He. We have studied solid 4He in two dimensions (2D) as function of the number
of vacancies n_v, up to 30, inserted in the initial configuration at rho =
0.0765 A^-2, close to the melting density, with the exact zero temperature
Shadow Path Integral Ground State method. The crystalline order is found to be
stable also in presence of many vacancies and we observe two completely
different regimes. For small n_v, up to about 6, vacancies form a bound state
and cause a decrease of the crystalline order. At larger n_v, the formation
energy of an extra vacancy at fixed density decreases by one order of magnitude
to about 0.6 K. In the equilibrated state it is no more possible to recognize
vacancies because they mainly transform into quantum dislocations and
crystalline order is found almost independent on how many vacancies have been
inserted in the initial configuration. The one--body density matrix in this
latter regime shows a non decaying large distance tail: dislocations, that in
2D are point defects, turn out to be mobile, their number is fluctuating, and
they are able to induce exchanges of particles across the system mainly
triggered by the dislocation cores. These results indicate that the notion of
incommensurate versus commensurate state loses meaning for solid 4He in 2D,
because the number of lattice sites becomes ill defined when the system is not
commensurate. Crystalline order is found to be stable also in 3D in presence of
up to 100 vacancies
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