Fermion bag approach to the sign problem in strongly coupled lattice QED with Wilson fermions

  • Shailesh Chandrasekharan
  • Anyi LiEmail author


We explore the sign problem in strongly coupled lattice QED with one flavor of Wilson fermions in four dimensions using the fermion bag formulation. We construct rules to compute the weight of a fermion bag and show that even though the fermions are confined into bosons, fermion bags with negative weights do exist. By classifying fermion bags as either simple or complex, we find numerical evidence that large complex bags with positive and negative weights come with equal probabilities. On the other hand simple bags have a large probability of having a positive weight. In analogy with the meron cluster approach, we suggest that eliminating the complex bags from the partition function should alleviate the sign problem while capturing the important physics. We also find a modified model containing only simple bags which does not suffer from any sign problem and argue that it contains a parity breaking phase transition similar to the original model. We also prove that when the hopping parameter is strictly infinite all fermion bags are non-negative.


Lattice QCD Lattice Gauge Field Theories Lattice Quantum Field Theory QCD 


  1. [1]
    R. Subedi et al., Probing cold dense nuclear matter, Science 320 (2008) 1476 [arXiv:0908.1514] [SPIRES].CrossRefADSGoogle Scholar
  2. [2]
    G.K. Campbell at. al., Probing interactions between ultracold fermions, Science 324 (2009) 360 [arXiv:0902.2558].CrossRefADSGoogle Scholar
  3. [3]
    J. Zaanen, Quantum critical electron systems: the uncharted sign worlds, Science 319 (2008) 1205. CrossRefADSGoogle Scholar
  4. [4]
    M. Cubrovic, J. Zaanen and K. Schalm, String theory, quantum phase transitions and the emergent Fermi-liquid, Science 325 (2009) 439 [arXiv:0904.1993] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  5. [5]
    M. Troyer and U.-J. Wiese, Computational complexity and fundamental limitations to fermionic quantum MonteCarlo simulations, Phys. Rev. Lett. 94 (2005) 170201 [cond-mat/0408370] [SPIRES].CrossRefADSGoogle Scholar
  6. [6]
    G. Aarts, Can stochastic quantization evade the sign problem? — the relativistic Bose gas at finite chemical potential, Phys. Rev. Lett. 102 (2009) 131601 [arXiv:0810.2089] [SPIRES].CrossRefADSGoogle Scholar
  7. [7]
    M.G. Endres, Method for simulating O(N) lattice models at finite density, Phys. Rev. D 75 (2007) 065012 [hep-lat/0610029] [SPIRES].ADSGoogle Scholar
  8. [8]
    S. Chandrasekharan, A new computational approach to lattice quantum field theories, PoS(LATTICE 2008)003 [arXiv:0810.2419] [SPIRES].
  9. [9]
    R.T. Scalettar, D.J. Scalapino and R.L. Sugar, New algorithm for the numerical simulation of fermions, Phys. Rev. B 34 (1986) 7911 [SPIRES].ADSGoogle Scholar
  10. [10]
    S. Duane, A.D. Kennedy, B.J. Pendleton and D. Roweth, Hybrid MonteCarlo, Phys. Lett. B 195 (1987) 216 [SPIRES].ADSGoogle Scholar
  11. [11]
    M. Lüscher, Computational strategies in lattice QCD, arXiv:1002.4232 [SPIRES].
  12. [12]
    F. Karsch and K.H. Mutter, Strong coupling QCD at finite baryon number density, Nucl. Phys. B 313 (1989) 541 [SPIRES].CrossRefADSGoogle Scholar
  13. [13]
    S. Chandrasekharan and U.-J. Wiese, Meron-cluster solution of a fermion sign problem, Phys. Rev. Lett. 83 (1999) 3116 [cond-mat/9902128] [SPIRES].CrossRefADSGoogle Scholar
  14. [14]
    M. Salmhofer, Equivalence of the strongly coupled lattice Schwinger model and the eight vertex model, Nucl. Phys. B 362 (1991) 641 [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  15. [15]
    C. Gattringer, V. Hermann and M. Limmer, Fermion loop simulation of the lattice Gross-Neveu model, Phys. Rev. D 76 (2007) 014503 [arXiv:0704.2277] [SPIRES].ADSGoogle Scholar
  16. [16]
    U. Wolff, Cluster simulation of relativistic fermions in two space-time dimensions, Nucl. Phys. B 789 (2008) 258 [arXiv:0707.2872] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  17. [17]
    U. Wolff, Simulating the all-order hopping expansion II: Wilson fermions, Nucl. Phys. B 814 (2009) 549 [arXiv:0812.0677] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  18. [18]
    U. Wenger, Efficient simulation of relativistic fermions via vertex models, Phys. Rev. D 80 (2009) 071503 [arXiv:0812.3565] [SPIRES].ADSGoogle Scholar
  19. [19]
    S. Chandrasekharan, The fermion bag approach to lattice field theories, Phys. Rev. D 82 (2010) 025007 [arXiv:0910.5736] [SPIRES].ADSGoogle Scholar
  20. [20]
    D.H. Adams and S. Chandrasekharan, Chiral limit of strongly coupled lattice gauge theories, Nucl. Phys. B 662 (2003) 220 [hep-lat/0303003] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  21. [21]
    I.O. Stamatescu, A note on the lattice fermionic determinant, Phys. Rev. D 25 (1982) 1130 [SPIRES].MathSciNetADSGoogle Scholar
  22. [22]
    C. Vafa and E. Witten, Restrictions on symmetry breaking in vector-like gauge theories, Nucl. Phys. B 234 (1984) 173 [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  23. [23]
    S. Aoki, New phase structure for lattice QCD with Wilson fermions, Phys. Rev. D 30 (1984) 2653 [SPIRES].ADSGoogle Scholar
  24. [24]
    D.J. Cecile and S. Chandrasekharan, Modeling pion physics in the ϵ-regime of two-flavor QCD using strong coupling lattice QED, Phys. Rev. D 77 (2008) 014506 [arXiv:0708.0558] [SPIRES].ADSGoogle Scholar

Copyright information

© SISSA, Trieste, Italy 2011

Authors and Affiliations

  1. 1.Department of PhysicsDuke UniversityDurhamU.S.A.

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