Equation of State at Finite Density from Imaginary Chemical Potential

We perform two flavor QCD simulations with an imaginary chemical potential and measure derivatives of the pressure up to 4th order as a function of the imaginary chemical potential and the temperature $T \in [0.83 T_c, 2 T_c]$. For temperatures $T \geq T_c$, these derivatives are fitted by a Taylor series in $\mu/T$ about $\mu=0$. A fit limited to 4th order describes the data poorly at all 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 a computational advantage over the direct measurement of Taylor coefficients at $\mu=0$. At temperatures $T \leq T_c$, we fit our data with a hadron resonance gas ansatz. The fit starts to fail at $T \gtrsim 0.95 T_c$. Using our fits, we also reconstruct the equation of state as a function of real quark and isospin chemical potentials.