Abstract.
Multi-level Monte Carlo sampling techniques exploit the locality of quantum field theory to provide a solution in purely-bosonic quantum field theories to the signal-to-noise ratio problem that affects the lattice determination of a large class of quantities. However, it is not straightforward to generalize multi-level sampling to lattice theories with fermionic content, such as QCD, due to the loss of manifest locality after the fermion path integral is performed. We discuss how the decrease of the fermion propagator with Euclidean distance induces a systematic approximation of the fermion propagator and the fermion determinant, in which the gauge field dependence of distant spacetime regions is completely factorized. This allows us to apply multi-level sampling to the lattice QCD computation of hadronic observables, such as mesonic and baryonic correlators. In particular, we show an application of this strategy to the disconnected contribution to the correlator of two flavour-singlet pseudoscalar densities, which results in a significant increase of the signal-to-noise ratio when a two-level sampling scheme is used.
Similar content being viewed by others
References
S. Durr et al., Science 322, 1224 (2008)
S. Borsanyi et al., Science 347, 1452 (2015)
D. Mohler, S. Schaefer, J. Simeth, EPJ Web of Conferences 175, 02010 (2018)
G. Parisi, Phys. Rep. 103, 203 (1984)
G.P. Lepage, The analysis of algorithms for lattice field theory, in Boulder ASI 1989 (1989) pp. 97--120
H.B. Meyer, H. Wittig, Prog. Part. Nucl. Phys. 104, 46 (2019)
O. Bär, Phys. Rev. 94, 054505 (2016)
G. Parisi, R. Petronzio, F. Rapuano, Phys. Lett. B 128, 418 (1983)
M. Lüscher, P. Weisz, JHEP 09, 010 (2001)
H.B. Meyer, JHEP 01, 048 (2003)
M. Della Morte, L. Giusti, Comput. Phys. Commun. 180, 813 (2009)
M. Della Morte, L. Giusti, Comput. Phys. Commun. 180, 819 (2009)
M. Della Morte, L. Giusti, JHEP 05, 056 (2011)
M. García Vera, S. Schaefer, Phys. Rev. D 93, 074502 (2016)
D.H. Weingarten, D.N. Petcher, Phys. Lett. B 99, 333 (1981)
M. Hasenbusch, Phys. Rev. D 59, 054505 (1999)
F. Knechtli, U. Wolff, Nucl. Phys. B 663, 3 (2003)
A. Hasenfratz, P. Hasenfratz, F. Niedermayer, Phys. Rev. D 72, 114508 (2005)
J. Finkenrath, F. Knechtli, B. Leder, Comput. Phys. Commun. 184, 1522 (2013)
S. Duane, A. Kennedy, B.J. Pendleton, D. Roweth, Phys. Lett. B 195, 216 (1987)
M. Cè, L. Giusti, S. Schaefer, Phys. Rev. D 93, 094507 (2016)
M. Cè, L. Giusti, S. Schaefer, Phys. Rev. D 95, 034503 (2017)
M. Cè, Solving the $\ab{U}_{A}(1)$ problem of QCD: new computational strategies and results, PhD thesis (Scuola Normale Superiore di Pisa, 2017)
M. Cè, C. Consonni, G.P. Engel, L. Giusti, Phys. Rev. D 92, 074502 (2015)
M. Cè, M. Garcia Vera, L. Giusti, S. Schaefer, Phys. Lett. B 762, 232 (2016)
E. Witten, Nucl. Phys. B 156, 269 (1979)
G. Veneziano, Nucl. Phys. B 159, 213 (1979)
K. Cichy, E. Garcia-Ramos, K. Jansen, K. Ottnad, C. Urbach, JHEP 09, 020 (2015)
P. Dimopoulos, arXiv:1812.08787 [hep-lat] (2018)
M. Cè, L. Giusti, S. Schaefer, PoS LATTICE2016, 263 (2017)
M. Cè, L. Giusti, S. Schaefer, EPJ Web of Conferences 175, 11005 (2018)
L. Giusti, P. Hernandez, M. Laine, P. Weisz, H. Wittig, JHEP 04, 013 (2004)
T. DeGrand, S. Schaefer, Comput. Phys. Commun. 159, 185 (2004)
S. Collins, G. Bali, A. Schäfer, PoS LATTICE2007, 141 (2007)
G.S. Bali, S. Collins, A. Schäfer, Comput. Phys. Commun. 181, 1570 (2010)
T. Blum, T. Izubuchi, E. Shintani, Phys. Rev. D 88, 094503 (2013)
M. Lüscher, Comput. Phys. Commun. 156, 209 (2004)
L. Giusti, M. Cè, S. Schaefer, EPJ Web of Conferences 175, 01003 (2018)
M. Guagnelli, R. Sommer, H. Wittig, Nucl. Phys. B 535, 389 (1998)
M. Lüscher, S. Schaefer, https://luscher.web.cern.ch/luscher/openQCD/
M. Lüscher, S. Schaefer, Comput. Phys. Commun. 184, 519 (2013)
C.R. Allton, V. Giménez, L. Giusti, F. Rapuano, Nucl. Phys. B 489, 427 (1997)
C. Thron, S.J. Dong, K.F. Liu, H.P. Ying, Phys. Rev. D 57, 1642 (1998)
C. McNeile, C. Michael, Phys. Rev. D 63, 114503 (2001)
R. Sommer, Nucl. Phys. B Proc. Suppl. 42, 186 (1995)
M. Foster, C. Michael, Phys. Rev. D 59, 074 (1999)
L. Giusti, T. Harris, A. Nada, S. Schaefer, in 36th International Symposium on Lattice Field Theory (Lattice 2018) East Lansing, MI, United States, July 22-28, 2018 Vol. LATTICE2018 (2018) p. 028
M. Lüscher, JHEP 07, 081 (2007)
M. Lüscher, Comput. Phys. Commun. 165, 199 (2005)
M. Lüscher, Schwarz factorization of the quark determinant, unpublished notes
H. Radjavi, J.P. Williams, Michigan Math. J. 16, 177 (1969)
P. Fritzsch et al., Nucl. Phys. B 865, 397 (2012)
M. Lüscher, Nucl. Phys. B 418, 637 (1994)
A. Boriçi, Ph. de Forcrand, Nucl. Phys. B 454, 645 (1995)
A. Boriçi, Ph. de Forcrand, Nucl. Phys. Proc. Suppl. 47, 800 (1996)
B. Jegerlehner, Nucl. Phys. B 465, 487 (1996)
B. Jegerlehner, Nucl. Phys. B Proc. Suppl. 42, 879 (1995)
M. Hasenbusch, Phys. Lett. B 519, 177 (2001)
M. Hasenbusch, K. Jansen, Nucl. Phys. Proc. Suppl. 106-107, 1076 (2002)
J.C. Sexton, D.H. Weingarten, Nucl. Phys. B 380, 665 (1992)
T.A. Manteuffel, Numer. Math. 28, 307 (1977)
Y. Saad, Iterative Methods for Sparse Linear Systems, second edition (SIAM, 2003)
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
The EPJ Publishers remain neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Cè, M. Locality and multi-level sampling with fermions. Eur. Phys. J. Plus 134, 299 (2019). https://doi.org/10.1140/epjp/i2019-12655-5
Received:
Accepted:
Published:
DOI: https://doi.org/10.1140/epjp/i2019-12655-5