A new way of determining the Lattice QCD equation of state at a finite chemical potential

Abstract

The Taylor expansion of thermodynamic observables at a finite baryon chemical potential ${\mu }_B$ is an oft-used method to circumvent the well-known sign problem of Lattice QCD. Owing to the associated difficulty and limitations of precision in calculating these high-ordered Taylor coefficients, it becomes essential to look for various resummation schemes which can mitigate the computational cost, besides providing trustworthy estimates of different thermodynamic observables. Recently, a way to exponentially resum the contribution of the first $N$ charge density correlation functions $D_1,\dots ,D_N$ to the Taylor series to all orders in ${\mu }_B$ was proposed in Phys. Rev. Lett. 128, 2, 022001 (2022). Since the correlation functions $D_n$ are calculated stochastically using estimates from different random volume sources, the resummation formulation gets affected by the biased estimates. These estimates can become very drastic and can radically misdirect the calculations for large values of $N$ and $\mu$ and also for observables which are higher order $\mu$ derivatives of free energy, specially at lower temperatures. In this work, we present a cumulant expansion procedure that allows to investigate and regulate these biased estimates at different orders in $\mu$. We find that the unbiased estimates in the cumulant expansion can truly capture the genuine higher-order stochastic fluctuations of the higher order correlation functions, which got suppressed by the exponential resummation formulation. Finally, we discover an unbiased formalism of the exponential resummation, which when expanded in a series, can exactly reproduce the Taylor series upto a desired power in $\mu$. We are also able to regain the knowledge of reweighting factor and many other important properties of the partition function, which got entirely lost through the implementation of cumulant expansion scheme.

9 pages, 8 figures, Contribution to The 39th International Symposium on Lattice Field Theory (Lattice 2022), minor changes, 2 new references added

References in corpus (13)

• The equation of state in (2+1)-flavor QCD
• Highly Improved Staggered Quarks on the Lattice, with Applications to Charm Physics
• The QCD Equation of State to $\mathcal{O}({\mu }_B^6)$ from Lattice QCD
• QCD at finite chemical potential with six time slices
• Lattice QCD equation of state at finite chemical potential from an alternative expansion scheme
• On the existence of the critical point in finite density lattice QCD
• Taylor expansions and Padé approximants for cumulants of conserved charge fluctuations at non-vanishing chemical potentials
• Second order cumulants of conserved charge fluctuations revisited I. Vanishing chemical potentials
• Reliable estimation of the radius of convergence in finite density QCD
• Lattice QCD Equation of State for Nonvanishing Chemical Potential by Resumming Taylor Expansion
• Implementation of the HMC algorithm on the tempered Lefschetz thimble method
• Apparent convergence of Padé approximants for the crossover line in finite density QCD
• New Way to Resum the Lattice QCD Taylor Series Equation of State at Finite Chemical Potential

Cited by in corpus (1)

• Estimates of Lee-Yang zeros and a possible critical point on the pion condensate boundary in the QCD isospin phase diagram using an unbiased exponential resummation on the lattice