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Finite density QCD via imaginary chemical potential

M. D'Elia, M. -P. Lombardo

TL;DR

This work leverages the imaginary chemical potential method to map the finite-density QCD phase diagram for four degenerate staggered flavors. By simulating in the $T$--$\mu_I$ plane, identifying the Roberge-Weiss structure and the endpoint where the RW line intersects the chiral transition, the authors perform a controlled analytic continuation to real $\mu$, extracting a quadratic dependence of the critical line in $\mu^2$ and translating it to physical units. The findings indicate a first-order chiral transition that coincides with deconfinement across a significant density range and show reasonable agreement with model predictions (Gross-Neveu and Random Matrix Theory) as well as with reweighting studies up to $\mu_B \sim 500$ MeV. Overall, the work demonstrates the viability of imaginary-$\mu$ techniques for constraining the QCD phase diagram at moderate densities and provides quantitative benchmarks for flavor dependence and transition order.

Abstract

We study QCD at nonzero temperature and baryon density in the framework of the analytic continuation from imaginary chemical potential. We carry out simulations of QCD with four flavor of staggered fermions, and reconstruct the phase diagram in the temperature-imaginary μplane. We consider ansätze for the analytic continuation of the critical line and other observables motivated both by theoretical considerations and mean field calculations in four fermion models and random matrix theory. We determine the critical line, and the analytic continuation of the chiral condensate, up to μ_B approx. 500 MeV. The results are in qualitative agreement with the predictions of model field theories, and consistent with a first order chiral transition. The correlation between the chiral transition and the deconfinement transition observed at μ=0 persists at nonzero density.

Finite density QCD via imaginary chemical potential

TL;DR

This work leverages the imaginary chemical potential method to map the finite-density QCD phase diagram for four degenerate staggered flavors. By simulating in the -- plane, identifying the Roberge-Weiss structure and the endpoint where the RW line intersects the chiral transition, the authors perform a controlled analytic continuation to real , extracting a quadratic dependence of the critical line in and translating it to physical units. The findings indicate a first-order chiral transition that coincides with deconfinement across a significant density range and show reasonable agreement with model predictions (Gross-Neveu and Random Matrix Theory) as well as with reweighting studies up to MeV. Overall, the work demonstrates the viability of imaginary- techniques for constraining the QCD phase diagram at moderate densities and provides quantitative benchmarks for flavor dependence and transition order.

Abstract

We study QCD at nonzero temperature and baryon density in the framework of the analytic continuation from imaginary chemical potential. We carry out simulations of QCD with four flavor of staggered fermions, and reconstruct the phase diagram in the temperature-imaginary μplane. We consider ansätze for the analytic continuation of the critical line and other observables motivated both by theoretical considerations and mean field calculations in four fermion models and random matrix theory. We determine the critical line, and the analytic continuation of the chiral condensate, up to μ_B approx. 500 MeV. The results are in qualitative agreement with the predictions of model field theories, and consistent with a first order chiral transition. The correlation between the chiral transition and the deconfinement transition observed at μ=0 persists at nonzero density.

Paper Structure

This paper contains 10 sections, 23 equations, 10 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Formalism and method
  3. The phase diagram in the imaginary $\mu$ -- temperature space
  4. From imaginary to real $\mu$ and the critical line in the $T,\mu^2$ plane
  5. The Gross-Neveu model
  6. Random Matrix Theories
  7. The critical line for the four flavor model
  8. Chiral condensate
  9. Nature of the chiral phase transtition
  10. Summary

Figures (10)

  • Figure 1: Average value of the Polyakov loop phase as a function of the imaginary chemical potential for different values of $\beta$. The vertical dashed line corresponds to $\theta = \mu_I/T = \pi/3$.
  • Figure 2: Average value of the chiral condensate as a function of the imaginary chemical potential for different values of $\beta$. The vertical dashed lines correspond to $\theta = \mu_I/T = (2 k + 1) \pi/3$. The continuous line in the lower picture is the result of a quadratic fit at small values of $a \mu_I$ obtained at $\beta = 5.10$.
  • Figure 3: Imaginary part of the barion density as a function of $\mu_I$ for different values of $\beta$ (left--hand side), and as a function of $\beta$ at $\theta = \mu_I/T = \frac{\pi}{3}^-$ (right-hand side).
  • Figure 4: Chiral condensate (white circles) and absolute value of the Polyakov loop (black circles) as a function of $\beta$ for $\theta = \pi/3$. The sharp changes of the two quantities coincide with the location of endpoint of the RW critical line.
  • Figure 5: Sketch of the phase diagram in the $\mu_I$--$\beta$ plane. The filled cirles represents direct determinations of the chiral critical line location from our simulations. The rest of the chiral line has been obtained by interpolation and by exploiting the symmetries of the partition function.
  • ...and 5 more figures