Tuning HMC using Poisson brackets

Details Tuning HMC using Poisson brackets Tuning HMC using Poisson brackets

2008-10-07

arxiv.org/abs/0810.1315v1

PoS LATTICE2008:041,2008

Physics

High Energy Physics

High Energy Physics - Lattice

7 pages, 4 figures, poster presented at the XXVI International Symposium on Lattice Field Theory, July 14-19, 2008, Williamsbu

Scientific paper

We discuss how the integrators used for the Hybrid Monte Carlo (HMC) algorithm not only approximately conserve some Hamiltonian $H$ but exactly conserve a nearby shadow Hamiltonian (\tilde H), and how the difference $\Delta H \equiv \tilde H - H $ may be expressed as an expansion in Poisson brackets. By measuring average values of these Poisson brackets over the equilibrium distribution $\propto e^{-H}$ generated by HMC we can find the optimal integrator parameters from a single simulation. We show that a good way of doing this in practice is to minimize the variance of $\Delta H$ rather than its magnitude, as has been previously suggested. Some details of how to compute Poisson brackets for gauge and fermion fields, and for nested and force gradient integrators are also presented.

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