scholarly journals Solving the fermion sign problem in quantum Monte Carlo simulations by Majorana representation

2015 ◽  
Vol 91 (24) ◽  
Author(s):  
Zi-Xiang Li ◽  
Yi-Fan Jiang ◽  
Hong Yao
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Quantum Monte Carlo ◽  
Sign Problem ◽  
Majorana Representation ◽  
Quantum Monte Carlo Simulations

scholarly journals Efficient Quantum Monte Carlo simulations of highly frustrated magnets: the frustrated spin-1/2 ladder

2017 ◽  
Vol 3 (1) ◽  
Author(s):  
Stefan Wessel ◽  
Bruce Normand ◽  
Frédéric Mila ◽  
Andreas Honecker
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Quantum Monte Carlo ◽  
Spin Model ◽  
Quantum Spin ◽  
Thermodynamic Quantities ◽  
Temperature Regimes ◽  
Sign Problem ◽  
Frustrated Spin ◽  
Quantum Monte Carlo Simulations

Quantum Monte Carlo simulations provide one of the more powerful and versatile numerical approaches to condensed matter systems. However, their application to frustrated quantum spin models, in all relevant temperature regimes, is hamstrung by the infamous “sign problem.” Here we exploit the fact that the sign problem is basis-dependent. Recent studies have shown that passing to a dimer (two-site) basis eliminates the sign problem completely for a fully frustrated spin model on the two-leg ladder. We generalize this result to all partially frustrated two-leg spin-1/2 ladders, meaning those where the diagonal and leg couplings take any antiferromagnetic values. We find that, although the sign problem does reappear, it remains remarkably mild throughout the entire phase diagram. We explain this result and apply it to perform efficient quantum Monte Carlo simulations of frustrated ladders, obtaining accurate results for thermodynamic quantities such as the magnetic specific heat and susceptibility of ladders up to L = 200L=200 rungs (400 spins 1/2) and down to very low temperatures.

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