Numerical sign problem: Difference between revisions

Revision as of 17:31, 11 December 2023

Revision as of 17:41, 11 December 2023

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There are various proposals for solving systems with a severe sign problem:

* Contour deformation. The field space is complexified and the path integral contour is deformed from $<math>R^N$</math> to another $<math>N$</math>-dimensional manifold embedded in complex $<math>C^N$</math> space
<ref>{{
Cite journal |arxiv= 2007.05436 [hep-lat]
|doi=10.1103/RevModPhys.94.015006

|title=Complex paths around the sign problem

10.1103/PhysRevLett.94.170201 |pmid=15904269 |bibcode=2005PhRvL..94q0201T |title=Complex paths around the sign problem

|journal=Reviews od Modern Physics |volume=94 |pages=015006 |year=2022

|last1=Alexandru |first1=Andrei

|last1last2=Basar |first1first2=Gokce

|last1last3=Bedaque |first1first3=Paulo

|last1last4=Warrington |first1first4=Neill

}}</ref> .

* [[Meron (physics)|Meron]]-cluster algorithms. These achieve an exponential speed-up by decomposing the fermion world lines into clusters that contribute independently. Cluster algorithms have been developed for certain theories,<ref name='Wiese-cluster'>{{cite journal |doi=10.1103/PhysRevLett.83.3116 |arxiv=cond-mat/9902128 |bibcode=1999PhRvL..83.3116C |title=Meron-Cluster Solution of Fermion Sign Problems |journal=Physical Review Letters |volume=83 |issue=16 |pages=3116–3119 |year=1999 |last1=Chandrasekharan |first1=Shailesh |last2=Wiese |first2=Uwe-Jens|s2cid=119061060 }}</ref> but not for the Hubbard model of electrons, nor for [[Quantum chromodynamics|QCD]], the theory of quarks.