We study the QCD phase diagram in the strong coupling region with finite coupling and fluctuation effects. Elucidating the phase diagram structure in QCD is a big challenge,
but the sign problem in finite density lattice QCD make it difficult to perform precision ab initio calculations. The strong coupling lattice QCD is a promising machinery, in which the effective action is obtained by integrating the link variables analytically at a given order of the strong coupling expansion, then the sign problem is expected to be weakened.
We have investigated the QCD phase diagram at strong coupling in the mean field approximation [1], and recently we have examined the fluctuation effects in the strong coupling limit by using the auxiliary field Monte-Carlo (AFMC) method [2]. Compared with the mean field results, hadron phase is found to be suppressed (extended) at low (high) chemical potential. These results are consistent with those obtained in the monomer-dimer-polymer (MDP) simulation [3].
It is staightforward to include finite coupling effects in AFMC. Next-to-leading order (NLO) effective action terms proportional to $1/g^2$ appear from one plaquette configurations and are found to contain four-Fermi and eight-Fermi interactions of quarks. We can transform the effective action including $1/g^2$ terms into that in the bilinear form of quarks by using the extended Hubbard-Stratonovich (EHS) transformation. As a first step, we have performed a Monte-Carlo calculation with temporal plaquette configurations at $\mu=0$. The phase transition temperature is found to decrease at finite coupling [4] as found in the mean field approximation. Effective action terms from spatial plaquette configurations requires multi-step EHS transformations, and it seems that naive bosonization leads to a severer weight cancellation [4].
In the presentation, we first review the previous studies of strong coupling lattice QCD including those in the mean field treatment, MDP and AFMC methods. Next we discuss finite coupling and fluctuation effects. We also discuss the order of the phase transition based on the finite size scaling of the chiral susceptibility in the strong coupling limit. Several prescriptions to weaken the sign problem are also discussed.
[1] T. Z. Nakano, Kohtaroh Miura, Akira Ohnishi, Phys. Rev. D 83 (2011), 016014; T. Z. Nakano, K. Miura, A. Ohnishi, Prog. Theor. Phys. 123 (2010), 825; K. Miura, T. Z. Nakano, A. Ohnishi, Noboru Kawamoto, Phys. Rev. D 80 (2009), 074034.
[2] T. Ichihara, A. Ohnishi, T. Z. Nakano, arXiv:1401.4647 [hep-lat].
[3] W. Unger, P. de Forcrand, J. Phys. G38 (2011) 124190.
[4] T. Ichihara, A. Ohnishi, in preparation.