20,001 research outputs found
Split Hamiltonian Monte Carlo revisited
We study Hamiltonian Monte Carlo (HMC) samplers based on splitting the
Hamiltonian as , where is quadratic and
small. We show that, in general, such samplers suffer from stepsize
stability restrictions similar to those of algorithms based on the standard
leapfrog integrator. The restrictions may be circumvented by preconditioning
the dynamics. Numerical experiments show that, when the
splitting is combined with preconditioning, it is
possible to construct samplers far more efficient than standard leapfrog HMC.Comment: 25 pages, 6 figure
A discrete Hubbard-Stratonovich decomposition for general, fermionic two-body interactions
A scheme is presented to decompose the exponential of a two-body operator in
a discrete sum over exponentials of one-body operators. This discrete
decomposition can be used instead of the Hubbard-Stratonovich transformation in
auxiliary-field quantum Monte-Carlo methods. As an illustration, the
decomposition is applied to the Hubbard model, where it is equivalent to the
discrete Hubbard-Stratonovich transformation introduced by Hirsch, and to the
nuclear pairing Hamiltonian.Comment: 8 pages, includes 2 eps figures, to appear in Phys. Lett.
Non-local updates for quantum Monte Carlo simulations
We review the development of update schemes for quantum lattice models
simulated using world line quantum Monte Carlo algorithms. Starting from the
Suzuki-Trotter mapping we discuss limitations of local update algorithms and
highlight the main developments beyond Metropolis-style local updates: the
development of cluster algorithms, their generalization to continuous time, the
worm and directed-loop algorithms and finally a generalization of the flat
histogram method of Wang and Landau to quantum systems.Comment: 14 pages, article for the proceedings of the "The Monte Carlo Method
in the Physical Sciences: Celebrating the 50th Anniversary of the Metropolis
Algorithm", Los Alamos, June 9-11, 200
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