Built on

M. Fukuma, N. Matsumoto and N. Umeda, “Applying the tempered Lefschetz thimble method to the Hubbard model away from half filling,” Phys. Rev. D 100, no. 11, 114510 (2019) [arXiv:1906.04243 [cond-mat.str-el]]
Original
1906
Earlier work this paper cites.
M. Fukuma, N. Matsumoto and N. Umeda, “Implementation of the HMC algorithm on the tempered Lefschetz thimble method,” [arXiv:1912.13303 [hep-lat]]
Original
1912
Earlier work this paper cites.
G. Parisi, “On complex probabilities,” Phys. Lett. 131B, 393 (1983)
1983
Earlier work this paper cites.
J. R. Klauder, “Stochastic quantization,” Acta Phys. Austriaca Suppl. 25, 251-281 (1983)
1983
Earlier work this paper cites.
H. C. Andersen, “RATTLE: A “velocity” version of the SHAKE algorithm for molecular dynamics calculations,” J. Comput. Phys. 52, 24 (1983)
1983
Earlier work this paper cites.
J. R. Klauder, “Coherent state Langevin equations for canonical quantum systems with applications to the quantized Hall effect,” Phys. Rev. A 29, 2036-2047 (1984)
1984
Earlier work this paper cites.
R. H. Swendsen and J.-S. Wang, “Replica Monte Carlo simulation of spin-glasses,” Phys. Rev. Lett. 57 2607 (1986)
1986
Earlier work this paper cites.
Y. Saad and M. H. Schultz, “GMRES: A Generalized minimal residual algorithm for solving nonsymmetric linear systems,” SIAM J. Sci. and Stat. Comput. 7, 856 (1986)
1986
Earlier work this paper cites.
C. J. Geyer, “Markov chain Monte Carlo maximum likelihood,” in computing science and statistics:
1991
Earlier work this paper cites.
H. A. van der Vorst, “Bi-CGSTAB: A fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems,” SIAM J. Sci. and Stat. Comput. 13, 631 (1992)
1992
Earlier work this paper cites.
E. Marinari and G. Parisi, “Simulated tempering: A new Monte Carlo scheme,” Europhys. Lett. 19, 451-458 (1992) [hep-lat/9205018]
1992
Earlier work this paper cites.
B. J. Leimkuhler and R. D. Skeel, “Symplectic numerical integrators in constrained Hamiltonian systems,” J. Comput. Phys. 112, 117 (1994)
1994
Earlier work this paper cites.
K. Hukushima and K. Nemoto, “Exchange Monte Carlo method and application to spin glass simulations,” J. Phys. Soc. Jpn. 65, 1604 (1996)
1996
Earlier work this paper cites.

Similar

M. A. Stephanov, “Random matrix model of QCD at finite density and the nature of the quenched limit,” Phys. Rev. Lett. 76, 4472 (1996) [hep-lat/9604003]
1996
Cited alongside, same era.
M. A. Halasz, A. D. Jackson, R. E. Shrock, M. A. Stephanov and J. J. M. Verbaarschot, “On the phase diagram of QCD,” Phys. Rev. D 58, 096007 (1998) [hep-ph/9804290]
1998
Cited alongside, same era.
M. Fukuma, N. Matsumoto and N. Umeda, “Distance between configurations in MCMC simulations and the geometrical optimization of the tempering algorithms,” PoS LATTICE2019, 168 (2019) [arXiv:2001.02028 [hep-lat]]
Original
2001
Cited alongside, same era.
F. Wang and D. P. Landau, “Efficient, multiple-range random walk algorithm to calculate the density of states,” Phys. Rev. Lett. 86, no.10, 2050 (2001) [arXiv:cond-mat/0011174 [cond-mat.stat-mech]]
2001
Cited alongside, same era.

Then

K. Nagata, J. Nishimura and S. Shimasaki, “Argument for justification of the complex Langevin method and the condition for correct convergence,” Phys. Rev. D 94, no. 11, 114515 (2016) [arXiv:1606.07627 [hep-lat]]
Original
2016
Later among the works it cites.
A. Alexandru, G. Başar and P. Bedaque, “Monte Carlo algorithm for simulating fermions on Lefschetz thimbles,” Phys. Rev. D 93, no. 1, 014504 (2016) [arXiv:1510.03258 [hep-lat]]
Original
2016
Later among the works it cites.
A. Alexandru, G. Başar, P. F. Bedaque, G. W. Ridgway and N. C. Warrington, “Sign problem and Monte Carlo calculations beyond Lefschetz thimbles,” JHEP 1605, 053 (2016) [arXiv:1512.08764 [hep-lat]]
Original
2016
Later among the works it cites.
M. Fukuma and N. Umeda, “Parallel tempering algorithm for integration over Lefschetz thimbles,” PTEP 2017, no. 7, 073B01 (2017) [arXiv:1703.00861 [hep-lat]]
Original
2017
Later among the works it cites.

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2020

Worldvolume approach to the tempered Lefschetz thimble method

Fukuma, Masafumi, Matsumoto, Nobuyuki

Understand

As a solution towards the numerical sign problem, we propose a novel Hybrid Monte Carlo algorithm, in which molecular dynamics is performed on a continuum set of integration surfaces foliated by the antiholomorphic gradient flow ("the worldvolume of an integration surface").

This is an extension of the tempered Lefschetz thimble method (TLTM), and solves the sign and multimodal problems simultaneously as the original TLTM does.
Furthermore, in this new algorithm, one no longer needs to compute the Jacobian of the gradient flow in generating a configuration, and only needs to evaluate its phase upon measurement.
To demonstrate that this algorithm works correctly, we apply the algorithm to a chiral random matrix model, for which the complex Langevin method is known not to work.

Built on

M. Fukuma, N. Matsumoto and N. Umeda, “Applying the tempered Lefschetz thimble method to the Hubbard model away from half filling,” Phys. Rev. D 100, no. 11, 114510 (2019) [arXiv:1906.04243 [cond-mat.str-el]]
Original
1906
Earlier work this paper cites.
M. Fukuma, N. Matsumoto and N. Umeda, “Implementation of the HMC algorithm on the tempered Lefschetz thimble method,” [arXiv:1912.13303 [hep-lat]]
Original
1912
Earlier work this paper cites.
G. Parisi, “On complex probabilities,” Phys. Lett. 131B, 393 (1983)
1983
Earlier work this paper cites.
J. R. Klauder, “Stochastic quantization,” Acta Phys. Austriaca Suppl. 25, 251-281 (1983)
1983
Earlier work this paper cites.
H. C. Andersen, “RATTLE: A “velocity” version of the SHAKE algorithm for molecular dynamics calculations,” J. Comput. Phys. 52, 24 (1983)
1983
Earlier work this paper cites.
J. R. Klauder, “Coherent state Langevin equations for canonical quantum systems with applications to the quantized Hall effect,” Phys. Rev. A 29, 2036-2047 (1984)
1984
Earlier work this paper cites.
R. H. Swendsen and J.-S. Wang, “Replica Monte Carlo simulation of spin-glasses,” Phys. Rev. Lett. 57 2607 (1986)
1986
Earlier work this paper cites.
Y. Saad and M. H. Schultz, “GMRES: A Generalized minimal residual algorithm for solving nonsymmetric linear systems,” SIAM J. Sci. and Stat. Comput. 7, 856 (1986)
1986
Earlier work this paper cites.
C. J. Geyer, “Markov chain Monte Carlo maximum likelihood,” in computing science and statistics:
1991
Earlier work this paper cites.
H. A. van der Vorst, “Bi-CGSTAB: A fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems,” SIAM J. Sci. and Stat. Comput. 13, 631 (1992)
1992
Earlier work this paper cites.
E. Marinari and G. Parisi, “Simulated tempering: A new Monte Carlo scheme,” Europhys. Lett. 19, 451-458 (1992) [hep-lat/9205018]
1992
Earlier work this paper cites.
B. J. Leimkuhler and R. D. Skeel, “Symplectic numerical integrators in constrained Hamiltonian systems,” J. Comput. Phys. 112, 117 (1994)
1994
Earlier work this paper cites.
K. Hukushima and K. Nemoto, “Exchange Monte Carlo method and application to spin glass simulations,” J. Phys. Soc. Jpn. 65, 1604 (1996)
1996
Earlier work this paper cites.

Similar

M. A. Stephanov, “Random matrix model of QCD at finite density and the nature of the quenched limit,” Phys. Rev. Lett. 76, 4472 (1996) [hep-lat/9604003]
1996
Cited alongside, same era.
M. A. Halasz, A. D. Jackson, R. E. Shrock, M. A. Stephanov and J. J. M. Verbaarschot, “On the phase diagram of QCD,” Phys. Rev. D 58, 096007 (1998) [hep-ph/9804290]
1998
Cited alongside, same era.
M. Fukuma, N. Matsumoto and N. Umeda, “Distance between configurations in MCMC simulations and the geometrical optimization of the tempering algorithms,” PoS LATTICE2019, 168 (2019) [arXiv:2001.02028 [hep-lat]]
Original
2001
Cited alongside, same era.
F. Wang and D. P. Landau, “Efficient, multiple-range random walk algorithm to calculate the density of states,” Phys. Rev. Lett. 86, no.10, 2050 (2001) [arXiv:cond-mat/0011174 [cond-mat.stat-mech]]
2001
Cited alongside, same era.

Then

K. Nagata, J. Nishimura and S. Shimasaki, “Argument for justification of the complex Langevin method and the condition for correct convergence,” Phys. Rev. D 94, no. 11, 114515 (2016) [arXiv:1606.07627 [hep-lat]]
Original
2016
Later among the works it cites.
A. Alexandru, G. Başar and P. Bedaque, “Monte Carlo algorithm for simulating fermions on Lefschetz thimbles,” Phys. Rev. D 93, no. 1, 014504 (2016) [arXiv:1510.03258 [hep-lat]]
Original
2016
Later among the works it cites.
A. Alexandru, G. Başar, P. F. Bedaque, G. W. Ridgway and N. C. Warrington, “Sign problem and Monte Carlo calculations beyond Lefschetz thimbles,” JHEP 1605, 053 (2016) [arXiv:1512.08764 [hep-lat]]
Original
2016
Later among the works it cites.
M. Fukuma and N. Umeda, “Parallel tempering algorithm for integration over Lefschetz thimbles,” PTEP 2017, no. 7, 073B01 (2017) [arXiv:1703.00861 [hep-lat]]
Original
2017
Later among the works it cites.

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

G. Aarts, E. Seiler and I. O. Stamatescu, “The complex Langevin method: When can it be trusted?,” Phys. Rev. D 81, 054508 (2010) [arXiv:0912.3360 [hep-lat]]

Original

2010

Cited alongside, same era.

G. Aarts, F. A. James, E. Seiler and I. O. Stamatescu, “Complex Langevin: Etiology and diagnostics of its main problem,” Eur. Phys. J. C 71, 1756 (2011) [arXiv:1101.3270 [hep-lat]]

Original

2011

Cited alongside, same era.

E. Witten, “Analytic continuation of Chern-Simons theory,” AMS/IP Stud. Adv. Math. 50, 347-446 (2011) [arXiv:1001.2933 [hep-th]]

Original

2011

Cited alongside, same era.

L. Pollet, “Recent developments in Quantum Monte-Carlo simulations with applications for cold gases,” Rep. Prog. Phys. 75, 094501 (2012) [arXiv:1206.0781 [cond-mat.quant-gas]]

Original

2012

Cited alongside, same era.

M. Cristoforetti, F. Di Renzo and L. Scorzato, “New approach to the sign problem in quantum field theories: High density QCD on a Lefschetz thimble,” Phys. Rev. D 86, 074506 (2012) [arXiv:1205.3996 [hep-lat]]

Original

2012

Cited alongside, same era.

G. Aarts, L. Bongiovanni, E. Seiler, D. Sexty and I. O. Stamatescu, “Controlling complex Langevin dynamics at finite density,” Eur. Phys. J. A 49, 89 (2013) [arXiv:1303.6425 [hep-lat]]

Original

2013

Cited alongside, same era.

M. Cristoforetti, F. Di Renzo, A. Mukherjee and L. Scorzato, “Monte Carlo simulations on the Lefschetz thimble: Taming the sign problem,” Phys. Rev. D 88, no. 5, 051501(R) (2013) [arXiv:1303.7204 [hep-lat]]

Original

2013

Cited alongside, same era.

H. Fujii, D. Honda, M. Kato, Y. Kikukawa, S. Komatsu and T. Sano, “Hybrid Monte Carlo on Lefschetz thimbles - A study of the residual sign problem,” JHEP 1310, 147 (2013) [arXiv:1309.4371 [hep-lat]]

Original

2013

Cited alongside, same era.

A. Alexandru, G. Başar, P. F. Bedaque and N. C. Warrington, “Tempered transitions between thimbles,” Phys. Rev. D 96, no. 3, 034513 (2017) [arXiv:1703.02414 [hep-lat]]

Original

2017