Diffusion quantum Monte Carlo is introduced at an elementary level. We highlight the strengths of the method in addressing important issues associated with quantum many-body systems, such as those associated with the ground-state energy and pair-distribution function. 4He clusters trapped on a graphite surface are simulated as an example of the method. A sample program and documentation for developing simulation projects are provided.

1.
J. C.
Anderson
,
Quantum Monte Carlo: Origins, Development, Applications
(
Oxford U.P.
,
New York
,
2007
).
2.
M.
Troyer
and
U.-J.
Wiese
, “
Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
,”
Phys. Rev. Lett.
94
,
170201-1
4
(
2005
).
3.
G. E.
Volovik
,
The Universe in a Helium Droplet
(
Oxford U.P.
,
New York
,
2003
).
4.
D.
Sato
,
K.
Naruse
,
T.
Matsui
, and
H.
Fukuyama
, “
Observation of self-binding in monolayer 3He
,”
Phys. Rev. Lett.
109
,
235306-1
4
(
2012
).
5.
L. F.
Gomez
,
E.
Loginov
, and
A. F.
Vilesov
, “
Traces of vortices in superfluid helium droplets
,”
Phys. Rev. Lett.
108
,
155302-1
5
(
2012
).
6.
N.
Metropolis
,
A. W.
Rosenbluth
,
M. N.
Rosenbluth
,
A. H.
Teller
, and
E.
Teller
, “
Equation of state calculations by fast computing machines
,”
J. Chem. Phys.
21
,
1087
1092
(
1953
).
7.
T.
Pang
,
An Introduction to Computational Physics
, 2nd ed. (
Cambridge U.P.
,
Cambridge, UK
,
2006
), Chap. 10.
8.
W. L.
McMillan
, “
Ground state of liquid He4
,”
Phys. Rev.
138
,
A442
A451
(
1965
).
9.
C. J.
Umrigar
,
K. G.
Wilson
, and
J. W.
Wilkins
, “
Optimized trial wave functions for quantum Monte Carlo calculations
,”
Phys. Rev. Lett.
60
,
1719
1722
(
1988
).
10.
G. D.
Mahan
,
Many-Particle Physics
, 3rd ed. (
Kluwer Academic
,
New York
,
2000
), Chap. 11.
11.
H. W.
Jackson
and
E.
Feenberg
, “
Perturbation method for low states of a many-particle boson system
,”
Ann. Phys.
15
,
266
295
(
1961
).
12.
H. A.
Forbert
and
S. A.
Chin
, “
Fourth-order diffusion Monte Carlo algorithms for solving quantum many-body problems
,”
Phys. Rev. B
63
,
144518-1
8
(
2001
).
13.
G. E.
Astrakharchik
, “
Quantum Monte Carlo study of ultracold gases
,” Ph.D. thesis (
University of Trento, Italy
,
2004
).
14.
P. J.
Reynolds
,
D. M.
Ceperley
,
B. J.
Alder
, and
W. A.
Lester
, Jr.
, “
Fixed-node quantum Monte Carlo for molecules
,”
J. Chem. Phys.
77
,
5593
5603
(
1982
).
15.
F.
Joly
,
C.
Lhuillier
, and
B.
Brami
, “
The helium–graphite interaction
,”
Surf. Sci.
264
,
419
422
(
1992
).
16.
R. A.
Aziz
,
A. R.
Janzen
, and
M. R.
Moldover
, “
Ab initio calculations for helium: A standard for transport property measurements
,”
Phys. Rev. Lett.
74
,
1586
1589
(
1995
).
17.
J.
Wilks
and
D. S.
Betts
,
An Introduction to Liquid Helium
, 2nd ed. (
Clarendon
,
Oxford
,
1987
).
18.
H. R.
Glyde
,
Excitations in Liquid and Solid Helium
(
Clarendon Press
,
Oxford
,
1994
), p.
41
.
19.
K.
Carneiro
,
J.
Passel
,
W.
Thomlinson
, and
H.
Taub
, “
Neutron-diffraction study of the solid layers at the liquid-solid boundary in 4He films adsorbed on graphite
,”
Phys. Rev. B
24
,
1170
1176
(
1981
).
20.
D. S.
Greywall
, “
Heat capacity and the commensurate-incommensurate transition of 4He adsorbed on graphite
,”
Phys. Rev. B
47
,
309
318
(
1993
).
21.
S.
Giorgini
,
J.
Boronat
, and
J.
Casulleras
, “
Diffusion Monte Carlo study of two-dimensional liquid 4He
,”
Phys. Rev. B
54
,
6099
6102
(
1996
).
22.
A.
Sarsa
,
J.
Mur-Petit
,
A.
Polls
, and
J.
Navarro
, “
Two-dimensional clusters of liquid 4He
,”
Phys. Rev. B
68
,
224514-1
5
(
2003
).
23.
See supplementary material at http://dx.doi.org/10.1119/1.4890824 for the sample program.
24.
Y. P.
Zhang
,
C. H.
Cheng
,
J. T.
Kim
,
J.
Stanojevic
, and
E. E.
Eyler
, “
Dissociation energies of molecular hydrogen and the hydrogen molecular ion
,”
Phys. Rev. Lett.
92
,
203003-1
4
(
2004
).
25.
R. L.
Kelly
, “
Atomic and ionic spectrum lines below 2000 angstroms: Hydrogen through Krypton, Part I (H-Cr)
,”
J. Phys. Chem. Ref. Data
16
(
Suppl. No. 1
),
1
649
(
1987
); available at http://www.nist.gov/data/PDFfiles/jpcrdS1Vol16.pdf.

Supplementary Material

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