Abstract
We analyze the chiral phase transition of the Nambu-Jona-Lasinio model in the cold and dense region on the lattice, developing the Grassmann version of the anisotropic tensor renormalization group algorithm. The model is formulated with the Kogut-Susskind fermion action. We use the chiral condensate as an order parameter to investigate the restoration of the chiral symmetry. The first-order chiral phase transition is clearly observed in the dense region at vanishing temperature with μ/T ∼ O(103) on a large volume of V = 10244. We also present the results for the equation of state.
Highlights
We plot the D dependence of δ at μ = 2.875, which is near the phase transition point and μ = 4.0, which is in the dense region with the restored chiral symmetry, as we will see below
We investigate the chiral phase transition employing the chiral condensate χ(n)χ(n), as an order parameter, which is defined by χ(n)χ(n) = lim lim ln Z, m→0 V →∞ V ∂m in the cold region
We have investigated the restoration of the chiral symmetry of the NJL model in the dense region at very low temperature, employing the Kogut-Susskind fermion action on the extremely large lattice of V = 10244, which is in the thermodynamic limit at zero temperature, essentially
Summary
We use the Kogut-Susskind fermion to formulate the NJL model on the lattice. [23, 24], we define the model at finite chemical potential μ as. Χ(n) and χ(n) are Grassmann-valued fields without the Dirac structure. Where n = (n1, n2, n3, n4)(∈ Z4) specifies a position in the lattice Λ, with the lattice spacing a. Since they describe the Kogut-Susskind fermions, χ(n) and χ(n) are single-component Grassmann variables. Ην(n) is the staggered sign function defined by ην(n) = (−1)n1+···+nν−1 with η1(n) = 1. The partition function is defined in the ordinal manner:. Eq (2.1) is invariant under the following continuous chiral transformation: χ(n) → eiα (n)χ(n), χ(n) → χ(n)eiα (n).
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