Numerical sign problem: Difference between revisions

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The sign problem is one of the major unsolved problems in the physics of many-particle systems, impeding progress in many areas:
* Condensed matter physics. It prevents the numerical solution of systems with a high density of strongly-correlated electrons, such as the [[Hubbard model]].<ref>E. Loh et. al., "Sign problem in the numerical simulation of many-electron systems" [http://prb.aps.org/abstract/PRB/v41/i13/p9301_1 Phys. Rev. B 41, 9301–9307 (1990)]</ref>
* Nuclear physics. It prevents the ab-initio calculation of properties of [[nuclear matter]] and hence limits our understanding of [[atomic nucleus|nuclei]] and [[neutron star]]s.
* Particle physics. It prevents the use of [[Lattice QCD]] to predict the phases and properties of [[quark matter]].<ref name='Philipsen'>O. Philipsen, "Lattice calculations at non-zero chemical potential: The QCD phase diagram", [http://pos.sissa.it//archive/conferences/077/011/Confinement8_011.pdf PoS Confinement8 011 (2008)], Plenary talk at Quark Confinement and the Hadron Spectrum 8, Mainz, Germany, Sept 2008</ref>