# Equation of State at Finite Density from Imaginary Chemical Potential - High Energy Physics - Lattice

Abstract: We perform two flavor QCD simulations with an imaginary chemical potentialand measure derivatives of the pressure up to 4th order as a function of theimaginary chemical potential and the temperature $T \in 0.83 T c, 2 T c$. Fortemperatures $T \geq T c$, these derivatives are fitted by a Taylor series in$\mu-T$ about $\mu=0$. A fit limited to 4th order describes the data poorly atall temperatures, showing that we are sensitive to 6th order contributions.Similarly, a 6th order fit fails for temperatures $T c \leq T \leq 1.05 T c$,showing the need for 8th order terms. Thus, our method may offer acomputational advantage over the direct measurement of Taylor coefficients at$\mu=0$. At temperatures $T \leq T c$, we fit our data with a hadron resonancegas ansatz. The fit starts to fail at $T \gtrsim 0.95 T c$. Using our fits, wealso reconstruct the equation of state as a function of real quark and isospinchemical potentials.

Author: Tetsuya Takaishi, Philippe de Forcrand, Atsushi Nakamura

Source: https://arxiv.org/