In this paper we carry out a low-temperature scan of the phase diagram of dense two-color QCD with N f = 2 quarks. The study is conducted using lattice simulation with rooted staggered quarks. At small chemical potential we observe the hadronic phase, where the theory is in a confining state, chiral symmetry is broken, the baryon density is zero and there is no diquark condensate. At the critical point µ = mπ/2 we observe the expected second order transition to Bose-Einstein condensation of scalar diquarks. In this phase the system is still in confinement in conjunction with non-zero baryon density, but the chiral symmetry is restored in the chiral limit. We have also found that in the first two phases the system is well described by chiral perturbation theory. For larger values of the chemical potential the system turns into another phase, where the relevant degrees of freedom are fermions residing inside the Fermi sphere, and the diquark condensation takes place on the Fermi surface. In this phase the system is still in confinement, chiral symmetry is restored and the system is very similar to the quarkyonic state predicted by SU(Nc) theory at large Nc.

We study the electromagnetic conductivity of QGP in a magnetic background by lattice simulations with N f ¼ 2 þ 1 dynamical rooted 2-stout smeared staggered fermions at the physical point. We study the correlation functions of the electromagnetic currents at T ¼ 200, 250 MeV and use the Tikhonov approach to extract the conductivity. The conductivity is found to rise with the magnetic field in the parallel direction and to decrease in the transverse direction, giving evidence for both the chiral magnetic effect and the magnetoresistance phenomenon in QGP. We also estimate the chiral charge relaxation time in QGP.

We propose and test a new approach to computation of canonical partition functions in lattice QCD at finite density. We suggest a few steps procedure. We first compute numerically the quark number density for imaginary chemical potential iµqI . Then we restore the grand canonical partition function for imaginary chemical potential using fitting procedure for the quark number density. Finally we compute the canonical partition functions using high precision numerical Fourier transformation. Additionally we compute the canonical partition functions using known method of the hopping parameter expansion and compare results obtained by two methods in the deconfining as well as in the confining phases. The agreement between two methods indicates the validity of the new method. Our numerical results are obtained in two flavor lattice QCD with clover improved Wilson fermions.