Summary
I will review the progress toward a finite baryon density algorithm in the canonical ensemble approach which entails particle number projection from the fermion determinant. These include an efficient Padé-Z2 stochastic estimator of the Tr log of the fermion matrix and a Noisy Monte Carlo update to accommodate unbiased estimate of the probability. Finally, I will propose a Hybrid Noisy Monte Carlo algorithm to reduce the large fluctuation in the estimated Tr log due to the gauge field which should improve the acceptance rate. Other application such as treating u and d as two separate flavors is discussed.
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References
For a review, see for example, S. D. Katz, hep-lat/0310051.
I. M. Barbour, S. E. Morrison, E. G. Klepfish, J. B. Kogut, and M.-P. Lombardo, Nucl. Phys. (Proc. Suppl.) 60A, 220 (1998); I.M. Barbour, C.T.H. Davies, and Z. Sabeur, Phys. Lett. B215, 567 (1988).
M. Alford, Nucl. Phys. B (Proc. Suppl.) 73, 161 (1999).
Z. Fodor and S.D. Katz, Phys. Lett .B534, 87 (2002); JHEP 0203, 014 (2002).
C. R. Allton et al., Phys. Rev. D66, 074507 (2002).
E. Dagotto, A. Moreo, R. Sugar, and D. Toussaint, Phys. Rev. B41, 811 (1990).
N. Weiss, Phys. Rev. D35, 2495 (1987); A. Hasenfratz and D. Toussaint, Nucl. Phys. B371, 539 (1992).
M. Alford, A. Kapustin, and F. Wilczek, Phys. Rev. D59, 054502 (2000).
P. deForcrand and O. Philipsen, Nucl. Phys. B642, 290 (2002); ibid, B673, 170 (2003).
M. D’Elia and M.-P. Lombardo, Phys. Rev. D67, 014505 (2003).
K.F. Liu, Int. Jour. Mod. Phys. B16, 2017 (2002).
M. Faber, O. Borisenko, S. Mashkevich, and G. Zinovjev, Nucl. Phys. B444, 563 (1995).
M. Faber, O. Borisenko, S. Mashkevich, and G. Zinovjev, Nucl. Phys. B (Proc. Suppl.) 42, 484 (1995).
For reviews on the subject see for example C.W. Wong, Phys. Rep. 15C, 285 (1975); D.J.Rowe, Nuclear Collective Motion, Methuen (1970); P. Ring and P. Schuck, The Nuclear Many-Body Problem, Springer-Verlag (1980).
H.D. Zeh, Z. Phys. 188, 361 (1965).
H. Rouhaninejad and J. Yoccoz, Nucl. Phys. 78, 353 (1966).
R.E. Peierls and J. Yoccoz, Proc. Phys. Soc. (London) A70, 381 (1957).
L. Lin, K. F. Liu, and J. Sloan, Phys. Rev. D61, 074505 (2000), [heplat/ 9905033]
C. Thron, S. J. Dong, K. F. Liu, H. P. Ying, Phys. Rev. D57, 1642 (1998); K.F. Liu, Chin. J. Phys. 38, 605 (2000).
S. J. Dong and K. F. Liu, Phys. Lett. B 328, 130 (1994).
B. Joó, I. Horváth, and K.F. Liu, Phys. Rev. D67, 074505 (2003).
G. Bhanot, A. D. Kennedy, Phys. Lett. 157B, 70 (1985).
S. Bernardson, P. McCarty and C. Thron, Comp. Phys. Commun. 78, 256 (1994).
S.J. Dong, J.-F. Lagaë, and K.F. Liu, Phys. Rev. Lett. 75, 2096 (1995); S.J. Dong, J.-F. Lagaë, and K.F. Liu, Phys. Rev. D54, 5496 (1996); S.J. Dong, K.F. Liu, and A. G. Williams, Phys. Rev. D58, 074504 (1998).
J.C. Sexton and D.H. Weingarten, Nucl. Phys. B(Proc. Suppl.) 42, 361 (1995).
M. Faber, private communication.
I. Horváth, A. Kennedy, and S. Sint, Nucl. Phys. B(Proc. Suppl.) 73, 834 (1999).
M. Clark and A. Kennedy, hep-lat/0309084.
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Liu, KF. (2005). A Finite Baryon Density Algorithm. In: Bori~i, A., Frommer, A., Joó, B., Kennedy, A., Pendleton, B. (eds) QCD and Numerical Analysis III. Lecture Notes in Computational Science and Engineering, vol 47. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-28504-0_10
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DOI: https://doi.org/10.1007/3-540-28504-0_10
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