- Auxiliary field Monte Carlo
**Auxiliary field Monte Carlo**is a method that allows the calculation, by use of Monte Carlo techniques, of averages of operators in many-body quantum mechanical (Blankenbecler 1981, Ceperley 1977) or classical problems (Baeurle 2004, Baeurle 2003, Baeurle 2002a).The distinctive ingredient of this method is the fact that the interactions are decoupled by means of the application of the

Hubbard-Stratonovich transformation , which permits to reformulate the many-body theory in terms of a scalar auxiliary field representation. This causes that the many-body problem is reduced to the calculation of a sum or integral over all possibleauxiliary field configurations. In this sense, there is a trade off: instead of dealing with one very complicated many-body problem, one faces the calculation of an infinite number of simple external-field problems.**Reweighting procedure and numerical sign problem**It is here, as in other related methods, that Monte Carlo enters the game in the guise ofimportance sampling: the large sum over auxiliary field configurations is performed by sampling over the most important ones, with a certain

probability . Since such fieldtheories generally possess a complex or non-positive semidefinite weight function, onehas to resort to a reweighting procedure, to get a positive definite reference distributionsuitable for Monte Carlo sampling. However, it is well-known that, in specific parameter ranges of the model under consideration, the oscillatory nature of the weight function can lead to a bad statistical convergence of the numerical integration procedure. The problem is known as thenumerical sign problem and can be alleviated with analytical and numerical convergence acceleration procedures (Baeurle 2002, Baeurle 2003a).**See also***

Quantum Monte Carlo **References*** cite journal

last = Blankenbecler

first = R.

coauthors = Scalapino, D. J. and Sugar, R. L.

title = Monte Carlo calculations of coupled boson-fermion systems. I

journal = Phys. Rev. D.

volume = 24

pages = 2278

year = 1981

url = http://link.aps.org/abstract/PRD/v24/p2278* cite journal

url = http://link.aps.org/abstract/PRB/v16/p3081

last = Ceperley

first = D.

coauthors = Chester, G.V. and Kalos, M.H.

title = Monte Carlo simulation of a many-fermion study

journal = Phys. Rev. B

volume = 16

pages = 3081

year = 1977* cite journal

url = http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TJ5-4BHK1JN-4&_user=616165&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_acct=C000032338&_version=1&_urlVersion=0&_userid=616165&md5=fe7a7f52aadb5375994112ee03cebefc

last = Baeurle

first = S.A.

title = Grand canonical auxiliary field Monte Carlo: a new technique for simulating open systems at high density

journal = Comput. Phys. Commun.

volume = 157

pages = 201

year = 2004* cite journal

url = http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6WHY-47MKK8M-2&_user=616165&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_acct=C000032338&_version=1&_urlVersion=0&_userid=616165&md5=60e4b8712970cf7e07a14b05c5f0e609

last = Baeurle

first = S.A.

title = Computation within the auxiliary field approach

journal = J. Comput. Phys.

volume = 184

pages = 540

year = 2003* cite journal |

url = http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=JCPSA6000117000007003027000001&idtype=cvips&gifs=yes

last = Baeurle

first = S.A.

coauthors = Martonak, R.; Parrinello, M.

title = A field-theoretical approach to simulation in the classical canonical and grand canonical ensemble

journal = J. Chem. Phys.

volume = 117

pages = 3027

year = 2002a* cite journal

url = http://prola.aps.org/abstract/PRL/v89/i8/e080602

last = Baeurle

first = S.A.

title = Method of Gaussian Equivalent Representation: A New Technique for Reducing the Sign Problem of Functional Integral Methods

journal = Phys. Rev. Lett.

volume = 89

pages = 080602

year = 2002* cite journal |

url = http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TJ5-48XCNNY-3&_user=616165&_coverDate=08%2F01%2F2003&_alid=745709877&_rdoc=6&_fmt=high&_orig=search&_cdi=5301&_sort=d&_docanchor=&view=c&_ct=8&_acct=C000032338&_version=1&_urlVersion=0&_userid=616165&md5=c5a0e9b03b74325c0dc7bf7d88406ecf

last = Baeurle

first = S.A.

title = The stationary phase auxiliary field Monte Carlo method: a new strategy for reducing the sign problem of auxiliary field methodologies

journal = Comput. Phys. Commun.

volume = 154

pages = 111

year = 2003a**External links*** [

*http://www-dick.chemie.uni-regensburg.de/group/stephan_baeurle/index.html Particle and Polymer Field Theory Group*]

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