Inhomogeneous Phases in the Chiral Gross-Neveu Model on the Lattice

Abstract

We discuss possible existence of inhomogeneous phase in low temperature and high density region in the 1+1 dimensional chiral Gross-Neveu ( $\chi$GN${}_2$ ) model on the lattice. First we investigate the phase structure of the $\chi$GN${}_2$ model at vanishing chemical potential, changing temperature. From behavior of ${\Delta }^2={\Sigma }^2+{\Pi }^2$ as a function of Monte Carlo time, a candidate of an order parameter for chiral symmetry in the $\chi$GN${}_2$ model is $\Delta$. At vanishing chemical potential, we observe restoration of chiral symmetry at high $T$. In low temperature and high chemical potential region, we find existence of inhomogeneous phase in spatial correlation functions of $\sigma$ and $\pi$. The signal of inhomogeneous phase in correlation function of $\Delta$ is more clearly than that of $\sigma$ or $\pi$.

Comments: 8 pages, 5 figures, The 38th International Symposium on Lattice Field Theory, LATTICE2021 26th-30th July, 2021