[Paper Review] Analytic Continuation in Two-color Finite Density QCD and Chiral Random Matrix Model

Yasuhiko Shinno, Hiroshi Yoneyama|ArXiv.org|Mar 5, 2009

Quantum Chromodynamics and Particle Interactions2 references3 citations

TL;DR

This paper investigates analytic continuation in two-color QCD using a chiral random matrix model (RMT) to assess the reliability of extrapolating observables from imaginary to real chemical potential. It finds that the ratio-type fitting function performs significantly better than polynomial fits at temperatures above the pseudo-critical point, consistent with Monte Carlo simulations, suggesting this behavior reflects non-trivial dynamics in the quark-gluon plasma.

ABSTRACT

Two-color finite density QCD is free from the sign problem, and it is thus regarded as a good model to check the validity of the analytic continuation method. We study the method in terms of the corresponding chiral random matrix model. It is found that at temperatures slightly higher than the pseudo critical temperature, the ratio type of extrapolated function works well in accordance with the results of the Monte Carlo simulations.

Motivation & Objective

• To evaluate the validity of analytic continuation methods in two-color QCD, which avoids the sign problem.
• To assess whether the chiral random matrix model (RMT) can reliably reproduce analytic continuation behavior observed in Monte Carlo simulations.
• To determine which fitting functions—polynomial or ratio-type—best describe the chiral condensate and pseudo-critical line across different temperature regimes.
• To examine the robustness of these results under improved RMT approximations that include all Matsubara frequencies.

Proposed method

• The study employs a chiral RMT model with temperature effects incorporated via the lowest Matsubara frequencies to simulate two-color QCD in the $μ$-$T$ plane.
• Phase structures are analyzed in both real and imaginary chemical potential regions, particularly near $μ = 0$.
• The chiral condensate and pseudo-critical line are analytically continued using polynomial and ratio-type fitting functions.
• The model is extended to include all Matsubara frequencies to test the sensitivity of results to the low-frequency approximation.
• Results are compared across three temperature regions: $T < T_D$, $T_D < T < T_{co}$, and $T > T_{co}$, defined by phase transition boundaries.
• The analysis focuses on convergence behavior and accuracy of extrapolated observables in the high-temperature regime.

Experimental results

Research questions

• RQ1 Does the ratio-type fitting function provide a more accurate analytic continuation of the chiral condensate than polynomial fits in two-color QCD at finite temperature?
• RQ2 How does the performance of fitting functions vary across different temperature regimes in the RMT framework?
• RQ3 Is the superior performance of the ratio-type fit in the high-temperature region robust when higher Matsubara frequencies are included?
• RQ4 To what extent does the absence of Roberge-Weiss symmetry in the RMT model affect analytic continuation results?

Key findings

• In the temperature region above the pseudo-critical point at $μ = 0$ (region III), the ratio-type fitting function shows fast and stable convergence for the chiral condensate, while polynomial fits exhibit slow convergence.
• The performance of the ratio-type function in region III matches the results of Monte Carlo simulations, indicating consistency with lattice QCD findings.
• When the RMT model is extended to include all Matsubara frequencies, the ratio-type fit still performs well in region III, confirming the robustness of this result against the low-frequency approximation.
• The RMT model's failure to capture the tricritical point and Roberge-Weiss symmetry limits its validity in low-temperature regions, but this does not affect the high-temperature conclusions.
• The analytic continuation of the pseudo-critical line also shows behavior consistent with Monte Carlo simulations, supporting the reliability of the ratio-type function.
• The results suggest that the superior performance of the ratio-type function reflects intrinsic non-trivial dynamics of the strongly correlated quark-gluon plasma at high temperatures.