Skip to main content

Fermion bag approach to fermion sign problems

New opportunities in lattice fermion field theories

The European Physical Journal A volume 49, Article number: 90 (2013) Cite this article

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.

This is a preview of subscription content, access via your institution.

Access options

Buy single article

Instant access to the full article PDF.

USD 39.95

Price includes VAT (USA)
Tax calculation will be finalised during checkout.

References

  1. M. Troyer, U.-J. Wiese, Phys. Rev. Lett. 94, 170201 (2005).

    ADS  Article  Google Scholar 

  2. J. Zaanen, Science 319, 1205 (2008).

    ADS  Article  Google Scholar 

  3. F. Fucito, E. Marinari, G. Parisi, C. Rebbi, Nucl. Phys. B 180, 369 (1981).

    MathSciNet  ADS  Article  Google Scholar 

  4. D.J. Scalapino, R.L. Sugar, Phys. Rev. Lett. 46, 519 (1981).

    MathSciNet  ADS  Article  Google Scholar 

  5. J.E. Hirsch, D.J. Scalapino, R.L. Sugar, R. Blankenbecler, Phys. Rev. Lett. 47, 1628 (1981).

    ADS  Article  Google Scholar 

  6. S. Chandrasekharan, Phys. Rev. D 82, 025007 (2010).

    ADS  Article  Google Scholar 

  7. S. Chandrasekharan, U.-J. Wiese, Phys. Rev. Lett. 83, 3116 (1999).

    ADS  Article  Google Scholar 

  8. A.N. Rubtsov, V.V. Savkin, A.I. Lichtenstein, Phys. Rev. B 72, 035122 (2005).

    ADS  Article  Google Scholar 

  9. E. Gull et al., Rev. Mod. Phys. 83, 349 (2011).

    ADS  Article  Google Scholar 

  10. S. Chandrasekharan, A. Li, Phys. Rev. Lett. 108, 140404 (2012).

    ADS  Article  Google Scholar 

  11. S. Chandrasekharan, PoS LATTICE2008, 003 (2008).

    Google Scholar 

  12. S. Chandrasekharan, A. Li, Phys. Rev. D 85, 091502 (2012).

    ADS  Article  Google Scholar 

  13. S. Chandrasekharan, Phys. Rev. D 86, 021701 (2012).

    ADS  Article  Google Scholar 

  14. D. Banerjee, S. Chandrasekharan, Phys. Rev. D 81, 125007 (2010).

    ADS  Article  Google Scholar 

  15. U. Wolff, Nucl. Phys. B 824, 254 (2010).

    MathSciNet  ADS  Article  MATH  Google Scholar 

  16. C. Gattringer, T. Kloiber, Nucl. Phys. B 869, 56 (2013).

    ADS  Article  MATH  Google Scholar 

  17. T. Appelquist, J. Terning, L. Wijewardhana, Phys. Rev. Lett. 77, 1214 (1996).

    ADS  Article  Google Scholar 

  18. B. Rosenstein, B. Warr, S. Park, Phys. Rep. 205, 59 (1991).

    ADS  Article  Google Scholar 

  19. J. Giedt, PoS LATTICE2012, 006 (2012).

    Google Scholar 

  20. E.T. Neil, PoS LATTICE2011, 009 (2011).

    Google Scholar 

  21. I.F. Herbut, Phys. Rev. Lett. 97, 146401 (2006).

    ADS  Article  Google Scholar 

  22. S. Hands, A. Kocić, J.B. Kogut, Ann. Phys. 224, 29 (1993).

    ADS  Article  Google Scholar 

  23. D.T. Son, Phys. Rev. B 75, 235423 (2007).

    ADS  Article  Google Scholar 

  24. J.E. Drut, D.T. Son, Phys. Rev. B 77, 075115 (2008).

    ADS  Article  Google Scholar 

  25. I.F. Herbut, V. Juričić, O. Vafek, Phys. Rev. B 80, 075432 (2009).

    ADS  Article  Google Scholar 

  26. V. Juričić, I.F. Herbut, G.W. Semenoff, Phys. Rev. B 80, 081405 (2009).

    ADS  Article  Google Scholar 

  27. L. Karkkainen, R. Lacaze, P. Lacock, B. Petersson, Nucl. Phys. B 415, 781 (1994).

    ADS  Article  Google Scholar 

  28. S. Hands, S. Kim, J.B. Kogut, Nucl. Phys. B 442, 364 (1995).

    ADS  Article  Google Scholar 

  29. E. Focht, J. Jersák, J. Paul, Phys. Rev. D 53, 4616 (1996).

    ADS  Article  Google Scholar 

  30. L. Del Debbio, S. Hands, Phys. Lett. B 373, 171 (1996).

    ADS  Article  Google Scholar 

  31. L. Del Debbio, S.J. Hands, J.C. Mehegan, Nucl. Phys. B 502, 269 (1997).

    ADS  Article  Google Scholar 

  32. I.M. Barbour, N. Psycharis, E. Focht, W. Franzki, J. Jersák, Phys. Rev. D 58, 074507 (1998).

    ADS  Article  Google Scholar 

  33. S. Christofi, C. Strouthos, JHEP 05, 088 (2007).

    ADS  Article  Google Scholar 

  34. J.E. Drut, T.A. Lähde, Phys. Rev. B 79, 241405 (2009).

    ADS  Article  Google Scholar 

  35. J.E. Drut, T.A. Lähde, Phys. Rev. Lett. 102, 026802 (2009).

    ADS  Article  Google Scholar 

  36. W. Armour, S. Hands, C. Strouthos, Phys. Rev. B 81, 125105 (2010).

    ADS  Article  Google Scholar 

  37. T. Paiva, R.T. Scalettar, W. Zheng, R.R.P. Singh, J. Oitmaa, Phys. Rev. B 72, 085123 (2005).

    ADS  Article  Google Scholar 

  38. Z.Y. Meng, T.C. Lang, S. Wessel, F.F. Assaad, A. Muramatsu, Nature 464, 847 (2010).

    ADS  Article  Google Scholar 

  39. S. Sorella, Y. Otsuka, S. Yunoki, Sci. Rep. 2, (2012).

  40. D.J. Scalapino, Rev. Mod. Phys. 84, 1383 (2012).

    ADS  Article  Google Scholar 

  41. D.J. Dean, M. Hjorth-Jensen, Rev. Mod. Phys. 75, 607 (2003).

    ADS  Article  Google Scholar 

  42. A.P. Mackenzie, Y. Maeno, Rev. Mod. Phys. 75, 657 (2003).

    ADS  Article  Google Scholar 

  43. V.Z. Kresin, S.A. Wolf, Rev. Mod. Phys. 81, 481 (2009).

    ADS  Article  Google Scholar 

  44. D. Lee, Prog. Part. Nucl. Phys. 63, 117 (2009).

    ADS  Article  Google Scholar 

  45. H. Yukawa, Proc. Phys. Math. Soc. Jpn. 17, 48 (1935).

    Google Scholar 

  46. P.F. Bedaque, U. van Kolck, Annu. Rev. Nucl. Part. Sci. 52, 339 (2002).

    ADS  Article  Google Scholar 

  47. E. Epelbaum, H.-W. Hammer, U.-G. Meissner, Rev. Mod. Phys. 81, 1773 (2009).

    ADS  Article  Google Scholar 

  48. D. Lee, B. Borasoy, T. Schäfer, Phys. Rev. C 70, 014007 (2004).

    ADS  Article  Google Scholar 

  49. E. Epelbaum, H. Krebs, D. Lee, U.-G. Meissner, Phys. Rev. Lett. 104, 142501 (2010).

    ADS  Article  Google Scholar 

  50. S. Fleming, T. Mehen, I.W. Stewart, Nucl. Phys. A 677, 313 (2000).

    ADS  Article  Google Scholar 

  51. S. Beane, P.F. Bedaque, M. Savage, U. van Kolck, Nucl. Phys. A 700, 377 (2002).

    ADS  Article  MATH  Google Scholar 

  52. K. Harada, H. Kubo, Y. Yamamoto, Phys. Rev. C 83, 034002 (2011).

    ADS  Article  Google Scholar 

  53. F. de Soto, J.C. Angles d’Auriac, J. Carbonell, Eur. Phys. J. A 47, 57 (2011).

    ADS  Article  Google Scholar 

  54. S. Chandrasekharan, M. Pepe, F. Steffen, U. Wiese, JHEP 12, 035 (2003).

    MathSciNet  ADS  Article  Google Scholar 

  55. S. Hands et al., Eur. Phys. J. C 17, 285 (2000).

    ADS  Article  MATH  Google Scholar 

  56. C. Wu, S.-C. Zhang, Phys. Rev. Lett. 93, 036403 (2004).

    ADS  Article  Google Scholar 

  57. D. Huertas-Hernando, F. Guinea, A. Brataas, Phys. Rev. B 74, 155426 (2006).

    ADS  Article  Google Scholar 

  58. M.G. Endres, Phys. Rev. Lett. 109, 250403 (2012).

    ADS  Article  Google Scholar 

  59. H. Evertz, Adv. Phys. 52, 1 (2003).

    ADS  Article  Google Scholar 

  60. J. Yoo, S. Chandrasekharan, R.K. Kaul, D. Ullmo, H.U. Baranger, Phys. Rev. B 71, 201309 (2005).

    ADS  Article  Google Scholar 

  61. N. Prokof’ev, B. Svistunov, Phys. Rev. Lett. 87, 160601 (2001).

    ADS  Article  Google Scholar 

  62. S. Chandrasekharan, A. Li, PoS LATTICE2011, 058 (2011).

    Google Scholar 

  63. S. Catterall, R. Galvez, J. Hubisz, D. Mehta, A. Veernala, Phys. Rev. D 86, 034502 (2012).

    ADS  Article  Google Scholar 

  64. I.-H. Lee, R.E. Shrock, Phys. Rev. Lett. 59, 14 (1987).

    ADS  Article  Google Scholar 

  65. G. Parisi, Nucl. Phys. B 100, 368 (1975).

    ADS  Article  Google Scholar 

  66. S. Hikami, T. Muta, Prog. Theor. Phys. 57, 785 (1977).

    ADS  Article  Google Scholar 

  67. S. Hands, Phys. Rev. D 51, 5816 (1995).

    ADS  Article  Google Scholar 

  68. M. Gomes, R.S. Mendes, R.F. Ribeiro, A.J. da Silva, Phys. Rev. D 43, 3516 (1991).

    ADS  Article  Google Scholar 

  69. K.-i. Kondo, Nucl. Phys. B 450, 251 (1995).

    MathSciNet  ADS  Article  MATH  Google Scholar 

  70. D.K. Hong, S.H. Park, Phys. Rev. D 49, 5507 (1994).

    ADS  Article  Google Scholar 

  71. M. Sugiura, Prog. Theor. Phys. 97, 311 (1997).

    MathSciNet  ADS  Article  Google Scholar 

  72. L. Janssen, H. Gies, Phys. Rev. D 86, 105007 (2012).

    ADS  Article  Google Scholar 

  73. L. Rosa, P. Vitale, C. Wetterich, Phys. Rev. Lett. 86, 958 (2001).

    ADS  Article  Google Scholar 

  74. A. Li, J. Phys. Conf. Ser. 432, 012024 (2013).

    ADS  Article  Google Scholar 

  75. B. Rosenstein, H.-L. Yu, A. Kovner, Phys. Lett. B 314, 381 (1993).

    ADS  Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Duke University, Box 90305, 27708, Durham, NC, USA

    Shailesh Chandrasekharan

Authors
  1. Shailesh Chandrasekharan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Shailesh Chandrasekharan.

Additional information

Contribution to the Topical Issue “Lattice Field Theory Methods in Hadron and Nuclear Physics” edited by Simon Hands and Hartmut Wittig.

Communicated by S. Hands

Rights and permissions

Reprints 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

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epja/i2013-13090-y

Keywords

  • Partition Function
  • Sign Problem
  • Chiral Symmetry
  • Pairing Mechanism
  • Solvable Form