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2018

Fourier acceleration, the HMC algorithm and renormalizability

Christ, Norman H., Wickenden, Evan W.

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The analysis developed by L\"uscher and Schaefer of the Hybrid Monte Carlo (HMC) algorithm is extended to include Fourier acceleration.

We show for the $\phi^4$ theory that Fourier acceleration substantially changes the structure of the theory for both the Langevin and HMC algorithms.
When expanded in perturbation theory, each five-dimensional auto-correlation function of the fields $\phi(x_i, t_i)$, $1\le i \le N $, corresponding to a specific 4-dimensional Feynman graph separates into two factors: one depending on the Monte-Carlo evolution times $t_i$ and the second depending on the space-time positions $x_i$.
This separation implies that only auto-correlation times at the lattice scale appear, eliminating critical slowing down in perturbation theory.

Fourier acceleration, the HMC algorithm and renormalizability · Around

Built on

G. Parisi and Y.-s. Wu, Perturbation Theory Without Gauge Fixing , Sci. Sin. 24
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G. G. Batrouni, G. R. Katz, A. S. Kronfeld, G. P. Lepage, B. Svetitsky and K. G. Wilson, Langevin Simulations of Lattice Field Theories , Phys. Rev. D32 (1985) 2736
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J. Zinn-Justin, Renormalization and Stochastic Quantization , Nucl. Phys. B275 (1986) 135
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S. Duane, A. D. Kennedy, B. J. Pendleton and D. Roweth, Hybrid Monte Carlo , Phys. Lett. B195 (1987) 216
1987
Earlier work this paper cites.

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M. Luscher and S. Schaefer, Non-renormalizability of the HMC algorithm , JHEP 04 (2011) 104 [ 1103.1810 ]
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Then

G. Cossu, P. Boyle, N. Christ, C. Jung, A. JÃ¼ttner and F. Sanfilippo, Testing algorithms for critical slowing down , EPJ Web Conf. 175 (2018) 02008 [ 1710.07036 ]
Original
2018
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X.-Y. Jin, Ensemble Quasi-Newton HMC , in Proceedings, 36th International Symposium on Lattice Field Theory (Lattice 2018) , vol. LATTICE2018, p. 027, 2018
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Y. Zhao, Testing a new gauge-fixed Fourier acceleration algorithm , in Proceedings, 36th International Symposium on Lattice Field Theory (Lattice 2018) , vol. LATTICE2018, p. 156, 2018
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Closest in time.

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