Numerical sign problem: Difference between revisions

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* [[Stochastic quantization]]. The sum over configurations is obtained as the equilibrium distribution of states explored by a complex [[Langevin equation]]. So far, the algorithm has been found to evade the sign problem in test models that have a sign problem but do not involve fermions.<ref>{{cite journal |doi=10.1103/PhysRevLett.102.131601 |pmid=19392346 |arxiv=0810.2089 |bibcode=2009PhRvL.102m1601A |title=Can Stochastic Quantization Evade the Sign Problem? The Relativistic Bose Gas at Finite Chemical Potential |journal=Physical Review Letters |volume=102 |issue=13 |pages=131601 |year=2009 |last1=Aarts |first1=Gert}}</ref>

* Fixed-node method. One fixes the ___location of nodes (zeros) of the multiparticle wavefunction, and uses Monte Carlo methods to obtain an estimate of the energy of the ground state, subject to that constraint.<ref>{{cite journal |doi=10.1103/PhysRevLett.72.2442 |pmid=10055881 |bibcode=1994PhRvL..72.2442V |title=Fixed-Node Quantum Monte Carlo Method for Lattice Fermions |journal=Physical Review Letters |volume=72 |issue=15 |pages=2442–2445 |year=1994 |last1=Van Bemmel |first1=H. J. M. |last2=Ten Haaf |first2=D. F. B. |last3=Van Saarloos |first3=W. |last4=Van Leeuwen |first4=J. M. J. |last5=An |first5=G. |hdl=1887/5478}}</ref>

* Majorana algorithms. Using Majorana fermion representation to perform Hubbard-StratenovichStratonovich transformations can help to solve the fermion sign problem of a class of fermionic many-body models.<ref>{{cite journal |doi=10.1103/PhysRevB.91.241117 |arxiv=1408.2269 |bibcode=2015PhRvB..91x1117L |title=Solving the fermion sign problem in quantum Monte Carlo simulations by Majorana representation |journal=Physical Review B |volume=91 |issue=24 |year=2015 |last1=Li |first1=Zi-Xiang |last2=Jiang |first2=Yi-Fan |last3=Yao |first3=Hong}}</ref><ref>{{Cite journal |doi=10.1103/PhysRevLett.117.267002 |pmid=28059531 |arxiv=1601.05780 |bibcode=2016PhRvL.117z7002L |title=Majorana-Time-Reversal Symmetries: A Fundamental Principle for Sign-Problem-Free Quantum Monte Carlo Simulations |journal=Physical Review Letters |volume=117 |issue=26 |pages=267002 |year=2016 |last1=Li |first1=Zi-Xiang |last2=Jiang |first2=Yi-Fan |last3=Yao |first3=Hong}}</ref>

==See also==