scholarly journals Alleviating the sign problem in quantum Monte Carlo simulations of spin-orbit-coupled multiorbital Hubbard models

2020 ◽  
Vol 101 (4) ◽  
Author(s):  
Aaram J. Kim ◽  
Philipp Werner ◽  
Roser Valentí
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Quantum Monte Carlo ◽  
Spin Orbit ◽  
Hubbard Models ◽  
Sign Problem ◽  
Quantum Monte Carlo Simulations

scholarly journals Hamming Distance and the onset of quantum criticality

2021 ◽  
Author(s):  
TianCheng Yi ◽  
Richard Scalettar ◽  
Rubem Mondaini
Keyword(s):  
Monte Carlo ◽  
Quantum Monte Carlo ◽  
Hamming Distance ◽  
Quantum Criticality ◽  
Significant Advance ◽  
Quantum Critical Points ◽  
Hubbard Models ◽  
Sign Problem ◽  
Quantum Monte Carlo Methods ◽  
Quantum Monte Carlo Simulations

Abstract Simulating models for quantum correlated matter unveils the inherent limitations of deterministic classical computations. In particular, in the case of quantum Monte Carlo methods, this is manifested by the emergence of negative weight configurations in the sampling, that is, the sign problem (SP). There have been several recent calculations which exploit the SP to locate underlying critical behavior. Here, utilizing a metric that quantifies phase-space ergodicity in such sampling, the Hamming distance, we suggest a significant advance on these ideas to extract the location of quantum critical points in various fermionic models, in spite of the presence of a severe SP. Combined with other methods, exact diagonalization in our case, it elucidates both the nature of the different phases as well as their location, as we demonstrate explicitly for the honeycomb and triangular Hubbard models, in both their U(1) and SU(2) forms. Our approach charts a path to circumvent inherent limitations imposed by the SP, allowing the exploration of the phase diagram of a variety of fermionic quantum models hitherto considered to be impractical via 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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