Abstract
The fermion bag approach is a new method to tackle fermion sign problems in lattice field theories. Using this approach it is possible to solve a class of sign problems that seem unsolvable by traditional methods. The new solutions emerge when partition functions are written in terms of fermion bags and bosonic worldlines. In these new variables it is possible to identify hidden pairing mechanisms which lead to the solutions. The new solutions allow us for the first time to use Monte Carlo methods to solve a variety of interesting lattice field theories, thus creating new opportunities for understanding strongly correlated fermion systems.
References
M. Troyer, U.-J. Wiese, Phys. Rev. Lett. 94, 170201 (2005).
J. Zaanen, Science 319, 1205 (2008).
F. Fucito, E. Marinari, G. Parisi, C. Rebbi, Nucl. Phys. B 180, 369 (1981).
D.J. Scalapino, R.L. Sugar, Phys. Rev. Lett. 46, 519 (1981).
J.E. Hirsch, D.J. Scalapino, R.L. Sugar, R. Blankenbecler, Phys. Rev. Lett. 47, 1628 (1981).
S. Chandrasekharan, Phys. Rev. D 82, 025007 (2010).
S. Chandrasekharan, U.-J. Wiese, Phys. Rev. Lett. 83, 3116 (1999).
A.N. Rubtsov, V.V. Savkin, A.I. Lichtenstein, Phys. Rev. B 72, 035122 (2005).
E. Gull et al., Rev. Mod. Phys. 83, 349 (2011).
S. Chandrasekharan, A. Li, Phys. Rev. Lett. 108, 140404 (2012).
S. Chandrasekharan, PoS LATTICE2008, 003 (2008).
S. Chandrasekharan, A. Li, Phys. Rev. D 85, 091502 (2012).
S. Chandrasekharan, Phys. Rev. D 86, 021701 (2012).
D. Banerjee, S. Chandrasekharan, Phys. Rev. D 81, 125007 (2010).
U. Wolff, Nucl. Phys. B 824, 254 (2010).
C. Gattringer, T. Kloiber, Nucl. Phys. B 869, 56 (2013).
T. Appelquist, J. Terning, L. Wijewardhana, Phys. Rev. Lett. 77, 1214 (1996).
B. Rosenstein, B. Warr, S. Park, Phys. Rep. 205, 59 (1991).
J. Giedt, PoS LATTICE2012, 006 (2012).
E.T. Neil, PoS LATTICE2011, 009 (2011).
I.F. Herbut, Phys. Rev. Lett. 97, 146401 (2006).
S. Hands, A. Kocić, J.B. Kogut, Ann. Phys. 224, 29 (1993).
D.T. Son, Phys. Rev. B 75, 235423 (2007).
J.E. Drut, D.T. Son, Phys. Rev. B 77, 075115 (2008).
I.F. Herbut, V. Juričić, O. Vafek, Phys. Rev. B 80, 075432 (2009).
V. Juričić, I.F. Herbut, G.W. Semenoff, Phys. Rev. B 80, 081405 (2009).
L. Karkkainen, R. Lacaze, P. Lacock, B. Petersson, Nucl. Phys. B 415, 781 (1994).
S. Hands, S. Kim, J.B. Kogut, Nucl. Phys. B 442, 364 (1995).
E. Focht, J. Jersák, J. Paul, Phys. Rev. D 53, 4616 (1996).
L. Del Debbio, S. Hands, Phys. Lett. B 373, 171 (1996).
L. Del Debbio, S.J. Hands, J.C. Mehegan, Nucl. Phys. B 502, 269 (1997).
I.M. Barbour, N. Psycharis, E. Focht, W. Franzki, J. Jersák, Phys. Rev. D 58, 074507 (1998).
S. Christofi, C. Strouthos, JHEP 05, 088 (2007).
J.E. Drut, T.A. Lähde, Phys. Rev. B 79, 241405 (2009).
J.E. Drut, T.A. Lähde, Phys. Rev. Lett. 102, 026802 (2009).
W. Armour, S. Hands, C. Strouthos, Phys. Rev. B 81, 125105 (2010).
T. Paiva, R.T. Scalettar, W. Zheng, R.R.P. Singh, J. Oitmaa, Phys. Rev. B 72, 085123 (2005).
Z.Y. Meng, T.C. Lang, S. Wessel, F.F. Assaad, A. Muramatsu, Nature 464, 847 (2010).
S. Sorella, Y. Otsuka, S. Yunoki, Sci. Rep. 2, (2012).
D.J. Scalapino, Rev. Mod. Phys. 84, 1383 (2012).
D.J. Dean, M. Hjorth-Jensen, Rev. Mod. Phys. 75, 607 (2003).
A.P. Mackenzie, Y. Maeno, Rev. Mod. Phys. 75, 657 (2003).
V.Z. Kresin, S.A. Wolf, Rev. Mod. Phys. 81, 481 (2009).
D. Lee, Prog. Part. Nucl. Phys. 63, 117 (2009).
H. Yukawa, Proc. Phys. Math. Soc. Jpn. 17, 48 (1935).
P.F. Bedaque, U. van Kolck, Annu. Rev. Nucl. Part. Sci. 52, 339 (2002).
E. Epelbaum, H.-W. Hammer, U.-G. Meissner, Rev. Mod. Phys. 81, 1773 (2009).
D. Lee, B. Borasoy, T. Schäfer, Phys. Rev. C 70, 014007 (2004).
E. Epelbaum, H. Krebs, D. Lee, U.-G. Meissner, Phys. Rev. Lett. 104, 142501 (2010).
S. Fleming, T. Mehen, I.W. Stewart, Nucl. Phys. A 677, 313 (2000).
S. Beane, P.F. Bedaque, M. Savage, U. van Kolck, Nucl. Phys. A 700, 377 (2002).
K. Harada, H. Kubo, Y. Yamamoto, Phys. Rev. C 83, 034002 (2011).
F. de Soto, J.C. Angles d’Auriac, J. Carbonell, Eur. Phys. J. A 47, 57 (2011).
S. Chandrasekharan, M. Pepe, F. Steffen, U. Wiese, JHEP 12, 035 (2003).
S. Hands et al., Eur. Phys. J. C 17, 285 (2000).
C. Wu, S.-C. Zhang, Phys. Rev. Lett. 93, 036403 (2004).
D. Huertas-Hernando, F. Guinea, A. Brataas, Phys. Rev. B 74, 155426 (2006).
M.G. Endres, Phys. Rev. Lett. 109, 250403 (2012).
H. Evertz, Adv. Phys. 52, 1 (2003).
J. Yoo, S. Chandrasekharan, R.K. Kaul, D. Ullmo, H.U. Baranger, Phys. Rev. B 71, 201309 (2005).
N. Prokof’ev, B. Svistunov, Phys. Rev. Lett. 87, 160601 (2001).
S. Chandrasekharan, A. Li, PoS LATTICE2011, 058 (2011).
S. Catterall, R. Galvez, J. Hubisz, D. Mehta, A. Veernala, Phys. Rev. D 86, 034502 (2012).
I.-H. Lee, R.E. Shrock, Phys. Rev. Lett. 59, 14 (1987).
G. Parisi, Nucl. Phys. B 100, 368 (1975).
S. Hikami, T. Muta, Prog. Theor. Phys. 57, 785 (1977).
S. Hands, Phys. Rev. D 51, 5816 (1995).
M. Gomes, R.S. Mendes, R.F. Ribeiro, A.J. da Silva, Phys. Rev. D 43, 3516 (1991).
K.-i. Kondo, Nucl. Phys. B 450, 251 (1995).
D.K. Hong, S.H. Park, Phys. Rev. D 49, 5507 (1994).
M. Sugiura, Prog. Theor. Phys. 97, 311 (1997).
L. Janssen, H. Gies, Phys. Rev. D 86, 105007 (2012).
L. Rosa, P. Vitale, C. Wetterich, Phys. Rev. Lett. 86, 958 (2001).
A. Li, J. Phys. Conf. Ser. 432, 012024 (2013).
B. Rosenstein, H.-L. Yu, A. Kovner, Phys. Lett. B 314, 381 (1993).
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by S. Hands
Contribution to the Topical Issue “Lattice Field Theory Methods in Hadron and Nuclear Physics” edited by Simon Hands and Hartmut Wittig.
Rights and permissions
About this article
Cite this article
Chandrasekharan, S. Fermion bag approach to fermion sign problems. Eur. Phys. J. A 49, 90 (2013). https://doi.org/10.1140/epja/i2013-13090-y
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1140/epja/i2013-13090-y