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Results on Finite Density QCD

I. M. Barbour, S. E. Morrison, E. G. Klepfish, J. B. Kogut, M. -P. Lombardo

TL;DR

This work analyzes lattice QCD at finite baryon density, highlighting the failure of the quenched approximation due to the complex fermion determinant and arguing for dynamical fermions to obtain a physical equation of state. It surveys the Glasgow method, Lee-Yang zeros, and alternative strategies for simulating μ ≠ 0 with dynamical fermions, testing them across strong and intermediate coupling regimes and in the U(1) Gross-Neveu model. Strong-coupling results show an onset near $μ \approx m_π/2$ and a structured pattern of thresholds (onset $μ_o$, critical $μ_c$, saturation $μ_s$) that align with mean-field expectations, while intermediate-coupling studies reveal $Z(3)$ tunnelling and mass-dependent onset behaviors. The Gross-Neveu model confirms that the true critical behavior is governed by Lee-Yang zeros rather than Goldstone modes, underscoring the central role of the complex-action sign problem and pointing to potential directions such as improved ensembles and four-fermion terms to access the chiral limit.

Abstract

A brief summary of the formulation of QCD at finite chemical potental, $μ$, is presented. The failure of the quenched approximation to the problem is reviewed. Results are presented for dynamical simulations of the theory at strong and intermediate couplings. We find that the problems associated with the quenched theory persist: the onset of non-zero quark number does seem to occur at a chemical potential $\approx { {m_π} \over 2}$. However analysis of the Lee-Yang zeros of the grand canonical partition function in the complex fugacity plane, ($e^{μ/T}$), does show signals of critical behaviour in the expected region of chemical potential. Results are presented for a simulation at finite density of the Gross-Neveu model on a $16^3$ lattice near to the chiral limit. Contrary to our simulations of QCD no pathologies were found when $μ$ passed through the value $m_π/2}$.

Results on Finite Density QCD

TL;DR

This work analyzes lattice QCD at finite baryon density, highlighting the failure of the quenched approximation due to the complex fermion determinant and arguing for dynamical fermions to obtain a physical equation of state. It surveys the Glasgow method, Lee-Yang zeros, and alternative strategies for simulating μ ≠ 0 with dynamical fermions, testing them across strong and intermediate coupling regimes and in the U(1) Gross-Neveu model. Strong-coupling results show an onset near and a structured pattern of thresholds (onset , critical , saturation ) that align with mean-field expectations, while intermediate-coupling studies reveal tunnelling and mass-dependent onset behaviors. The Gross-Neveu model confirms that the true critical behavior is governed by Lee-Yang zeros rather than Goldstone modes, underscoring the central role of the complex-action sign problem and pointing to potential directions such as improved ensembles and four-fermion terms to access the chiral limit.

Abstract

A brief summary of the formulation of QCD at finite chemical potental, , is presented. The failure of the quenched approximation to the problem is reviewed. Results are presented for dynamical simulations of the theory at strong and intermediate couplings. We find that the problems associated with the quenched theory persist: the onset of non-zero quark number does seem to occur at a chemical potential . However analysis of the Lee-Yang zeros of the grand canonical partition function in the complex fugacity plane, (), does show signals of critical behaviour in the expected region of chemical potential. Results are presented for a simulation at finite density of the Gross-Neveu model on a lattice near to the chiral limit. Contrary to our simulations of QCD no pathologies were found when passed through the value .

Paper Structure

This paper contains 18 sections, 31 equations, 14 figures.

Table of Contents

  1. Introduction
  2. Quenched Simulations
  3. Methods for Simulating QCD at $\mu \neq 0$ with Dynamical Fermions
  4. The Glasgow Method
  5. Lee-Yang Zeros
  6. Alternative Methods
  7. The Static Quark Model
  8. Lattice QCD at Strong Coupling
  9. Strong Coupling using the Glasgow Method
  10. Results at Strong Coupling
  11. Lattice QCD at Intermediate Coupling
  12. $Z(3)$ Tunnelling
  13. Simulations on $6^4$ and $8^4$ lattices at intermediate coupling
  14. The U(1) Gross-Neveu Model
  15. The Lattice Formulation
  16. ...and 3 more sections

Figures (14)

  • Figure 1: Histograms of the real parts of the eigenvalues and of the real part of the zeros in the complex $\mu$-plane at strong coupling and bare quark mass, $ma=0.08$ on a $6^4$ lattice.
  • Figure 2: Histogram of the real parts of the eigenvalues in the complex $\mu$-plane at strong coupling and bare quark mass, $ma=0.05$ on a $6^4$ lattice.
  • Figure 3: Histogram of the real parts of the zeros in the complex $\mu$-plane at strong coupling and bare quark mass, $ma=0.05$ on a $6^4$ lattice.
  • Figure 4: Histogram of the real parts of the eigenvalues in the complex $\mu$-plane at strong coupling and bare quark mass, $ma=0.5$ on a $6^4$ lattice.
  • Figure 5: Histogram of the real parts of the zeros in the complex $\mu$-plane at strong coupling and bare quark mass, $ma=0.5$ on a $6^4$ lattice.
  • ...and 9 more figures