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Springer eBooks

Monte Carlo Simulation of One Dimensional Quantum Systems

Robert L. Sugar

Published Jan 1, 1984• 1 citation
Publisher
DOI
10.1007/978-94-009-6384-9_12

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•Jul 5, 1991•0 citations
We describe a novel simulation method that eliminates the slowing-down problem in the Monte Carlo (MC) simulations of imaginary-time path integrals near the continuum limit. This method combines a stochastic blocking procedure with the multigrid method to rapidly accelerate the sampling of paths in a quantum MC simulation, making its dynamics more ergodic. The effectiveness and efficiency of this method are demonstrated for several one-dimensional quantum systems and compared to other standard and accelerated methods.
I present a new and efficient disconnected cluster decomposition to perform Monte Carlo Simulations based on the Trotter-Suzuki method for 1-d quantum systems. As opposed to the normal checkerboard world line algorithm this mapping allows one to simulate models with interactions up to next nearest neighbours or even one-dimensional double layers. I have used this cluster decomposition to simulate the one-dimensional t-J-J' model at α=J'/J=0.5 and have investigated the sign problem in this model. At half band filling the system is dimerised into singlet spin pairs when α=0.5 due to frustration. I believe that the spin gap is no longer present around quarter band filling