Dirac semimetals are recently discovered materials with low energy electronic excitation spectrum similar to the massless two favour 3+1 Dirac fermions. The interaction between quasiparticles in Dirac semimetals is instantaneous Coulomb with large effective coupling constant α ∼ 1. In this report we present results of study of the phase diagram of Dirac semimetals within lattice simulation with rooted staggered fermions. In particular, we calculate the chiral condensate as a function of effective coupling constant and Fermi velocity anisotropy and thus determine the position of semimetal-insulator transition in Dirac semimetals.

We present our results on the 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 = m π /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(N c ) theory at large N c .

This report is devoted to the study of temperature dependence of shear viscosity in SU(3)gluodynamics. To calculate shear viscosity we measured the correlation function of the energymomentum tensor T 12 T 12 for a set of temperatures in the region T /T c ∈ (0.9, 1.5). The measurements were carried out using multilevel algorithm which considerably improves the accuracy of the data. For determination of the shear viscosity two methods were used: physically motivated ansatz and non-parametrical Backus-Gilbert method. Both methods give consistent results. The calculation allows to determine temperature dependence of the ratio of shear viscosity to the entropy density η/s. 34th annual International Symposium on Lattice Field Theory

In the background of the strong magnetic field the vacuum is suggested to possess an electromagnetically superconducting phase characterised by the charged ρ-meson condensate. The ρ-meson condensate is inhomogeneous due to the presence of the string-like defects which are parallel to the magnetic field. In agreement with these expectations, we have observed the presence of the ρ-vortices in numerical simulations of the vacuum of the quenched two-color lattice QCD in strong magnetic field background. We have found that in the quenched QCD the ρ-vortices form a liquid.

The phase diagram of two-color QCD with non-zero chiral chemical potential is studied by means of lattice simulation. We focus on the influence of a chiral chemical potential on the confinement/deconfinement phase transition and the breaking/restoration of chiral symmetry. The simulation is carried out with dynamical staggered fermions without rooting. The dependences of the Polyakov loop, the chiral condensate and the corresponding susceptibilities on the chiral chemical potential and the temperature are presented. We present here the first results of simulations with three-color QCD. The critical temperature is observed to increase with increasing chiral chemical potential for both gauge groups.