Tensor renormalization group study of cold and dense QCD in the strong coupling limit

We study the phase structure of the (3+1)-dimensional cold and dense QCD with the Kogut--Susskind quark in the strong coupling limit using the tensor renormalization group method. The chiral and nuclear transitions are investigated by calculating the chiral condensate and the quark number density as a function of the chemical potential. For a fixed temporal extent $N_\tau=8$, we determine the critical quark masses $m_c^{\chi}$ and $m_c^{n}$ for the chiral condensate and the quark number density, respectively, at which the first-order phase transition terminates with the vanishing discontinuity in thermodynamic quantities. We find that both quantities at the same quark mass exhibit a discontinuity at the same chemical potential, and the resulting critical quark masses are consistent with each other. We also compare our results for the critical quark masses with those obtained from the Monte Carlo simulation in the dual formulation and from the mean-field analysis. We further confirm the first-order phase transition at finite quark mass on a $1024^4$ lattice, which is essentially in the thermodynamic limit at zero temperature, as expected from the mean-field analysis.