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Quantum Monte Carlo: What can random numbers tell us about correlated quantum systems?
Author(s) -
Rombouts S.,
Heyde K.
Publication year - 2003
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.200301787
Subject(s) - quantum monte carlo , statistical physics , monte carlo method , boson , fermion , imaginary time , physics , monte carlo method in statistical physics , pairing , path integral monte carlo , quantum , sign (mathematics) , diffusion monte carlo , path integral formulation , auxiliary field , antisymmetry , monte carlo molecular modeling , hybrid monte carlo , quantum mechanics , mathematics , quantum statistical mechanics , markov chain monte carlo , statistics , mathematical analysis , linguistics , superconductivity , philosophy , supersymmetric quantum mechanics
Over the past decades, quantum Monte Carlo methods have proven to be very valuable for the study of quantum‐mechanical many‐body systems. The basic ingredient of theses methods is a decomposition of the imaginary‐time evolution operator into path integrals. These paths can then be sampled using Monte Carlo techniques. Though very successful for bosons, these methods often have troubles in dealing with fermions: the fermionic antisymmetry leads to a ‘sign problem’. One approach, the auxiliary‐field method, has yielded slightly better results in dealing with the sign problem. Some recent developments on this method are highlighted. As a case study, it is applied to a pairing model for Fe nuclei, where indications are found for a phase transition related to nucleon–nucleon pairing.