scholarly journals Entanglement and the fermion sign problem in auxiliary field quantum Monte Carlo simulations

2016 ◽  
Vol 94 (7) ◽  
Author(s):  
Peter Broecker ◽  
Simon Trebst
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Quantum Monte Carlo ◽  
Auxiliary Field ◽  
Sign Problem ◽  
Quantum Monte Carlo Simulations

NEGATIVE WEIGHTS IN QUANTUM MONTE CARLO SIMULATIONS AT FINITE-TEMPERATURES USING THE AUXILIARY FIELD METHOD

1994 ◽  
Vol 05 (03) ◽  
pp. 599-613 ◽  
Author(s):  
J.E. GUBERNATIS ◽  
X.Y. ZHANG
Keyword(s):  
Monte Carlo ◽  
Quantum Monte Carlo ◽  
Topological Defects ◽  
Field Method ◽  
Monte Carlo Algorithm ◽  
Auxiliary Field ◽  
Sign Problem ◽  
Time Patterns ◽  
Ill Conditioned Matrices ◽  
Quantum Monte Carlo Simulations

We study the conditions under which negative weights (the sign problem) can exist in the finite-temperature, auxiliary field, quantum Monte Carlo algorithm of Blankenbecler, Scalapino, and Sugar. We specifically consider whether the sign problem arises from round-off error resulting from operations involving very ill-conditioned matrices or from topological defects in the auxiliary fields mirroring the space-time patterns of the physical fields. While we demonstrate these situations can generate negative weights, the results of our numerical tests suggest that these factors are most likely not the dominant sources of the problem. We also argue that the negative weights should not be considered as just a fermion problem. If it exists for the fermion problem, it will also exist for an analogous boson problem.

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