scholarly journals Amelioration for the Sign Problem: An Adiabatic Quantum Monte Carlo Algorithm

2021 ◽  
Vol 127 (21) ◽  
Author(s):  
Mohammad-Sadegh Vaezi ◽  
Amir-Reza Negari ◽  
Amin Moharramipour ◽  
Abolhassan Vaezi
Keyword(s):  
Monte Carlo ◽  
Quantum Monte Carlo ◽  
Monte Carlo Algorithm ◽  
Sign Problem

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.

NUMERICAL STABILITY AND THE SIGN PROBLEM IN THE DETERMINANT QUANTUM MONTE CARLO METHOD

2005 ◽  
Vol 16 (08) ◽  
pp. 1319-1327 ◽  
Author(s):  
E. Y. LOH ◽  
J. E. GUBERNATIS ◽  
R. T. SCALETTAR ◽  
S. R. WHITE ◽  
D. J. SCALAPINO ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Quantum Monte Carlo ◽  
Numerical Stability ◽  
Exact Diagonalization ◽  
Monte Carlo Algorithm ◽  
Numerical Accuracy ◽  
Numerical Errors ◽  
Sign Problem ◽  
Quantum Monte Carlo Method ◽  
D Wave

A recent paper by Matuttis and Ito questions the numerical accuracy of a widely-used fermion Monte Carlo algorithm. They also claim that the increase in the d-wave pairfield susceptibility χd(T) of a doped 4×4 Hubbard model at low temperature, previously found using this algorithm, is an artifact due to numerical errors. Here, we provide tests which show that this algorithm is numerically accurate and show that the simulation of χd for a 2×2 lattice agrees with exact diagonalization results. We also provide more complete data for χd on a 4×4 lattice that is consistent with our previous results.

scholarly journals Sign-Problem-Free Fermionic Quantum Monte Carlo: Developments and Applications

2019 ◽  
Vol 10 (1) ◽  
pp. 337-356 ◽  
Author(s):  
Zi-Xiang Li ◽  
Hong Yao
Keyword(s):  
Monte Carlo ◽  
Quantum Monte Carlo ◽  
Hot Spot ◽  
High Temperature Superconductors ◽  
System Size ◽  
Many Body ◽  
Broken Symmetries ◽  
Sign Problem ◽  
Universal Quantum ◽  
Many Body Systems

Reliable simulations of correlated quantum systems, including high-temperature superconductors and frustrated magnets, are increasingly desired nowadays to further our understanding of essential features in such systems. Quantum Monte Carlo (QMC) is a unique numerically exact and intrinsically unbiased method to simulate interacting quantum many-body systems. More importantly, when QMC simulations are free from the notorious fermion sign problem, they can reliably simulate interacting quantum models with large system size and low temperature to reveal low-energy physics such as spontaneously broken symmetries and universal quantum critical behaviors. Here, we concisely review recent progress made in developing new sign-problem-free QMC algorithms, including those employing Majorana representation and those utilizing hot-spot physics. We also discuss applications of these novel sign-problem-free QMC algorithms in simulations of various interesting quantum many-body models. Finally, we discuss possible future directions of designing sign-problem-free QMC methods.

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