QCD thermodynamics with dynamical chiral fermions

TL;DR

This work investigates thermal QCD using dynamical overlap fermions, which preserve chiral symmetry at finite lattice spacing. The authors employ fixed-topology simulations and the slab method to determine the topological susceptibility, then average chiral observables over topological sectors to study temperature dependence and crossover behavior. They also examine the Dirac spectrum of the overlap operator and report a pronounced near-zero peak near Tc, consistent with instanton-based explanations and requiring large volumes to observe. The results validate the use of overlap fermions for finite-temperature QCD studies and provide cross-checks against staggered-fermion results, with implications for chiral and axial symmetry restoration.

Abstract

We discuss properties of thermal Quantum Chromodynamics obtained by means of lattice simulations with overlap fermions. This fermion discretisation preserves chiral symmetry at finite lattice spacing. We present details of the formulation and results for the chiral observables. We determine the topological susceptibility from simulations at fixed global topological charge based on the slab method. Using the measured values of the topological susceptibility we sum the chiral observables over all topological sectors. The volume dependence of the chiral susceptibility is in agreement with the crossover nature of the thermal QCD phase transition. Additionally we discuss the spectrum of the overlap Dirac operator and its volume and temperature dependence. Presented results are obtained at the temporal lattice extent $N_t=8$.

Figures (6)

• Figure 1: Setup of the slab method. The global topological charge if fixed to $Q$, the topological charge of the subvolume $xV$ is $q$, in the rest part of the volume $(1-x)V$ topological charge is $Q-q$.
• Figure 2: Example of the $\langle q'^2\rangle$ as the function of the subvolume $x$. The temperature is $T=155$ MeV, aspect ratio $N_s/N_t=4$, the global topological charge is $Q=0$.
• Figure 3: Topological susceptibility $\chi^{1/4}$ as a function of temperature determined using the slab method on all three studied aspect ratios $N_s/N_t=3,4,5$ and its infinite volume extrapolation. Results of Borsanyi:2016ksw, based on the staggered fermions, are also presented.
• Figure 4: Renormalized chiral condensate (left) and chiral susceptiblity (right) summed over all topological sectors. Red points and lines correspond to the aspect ratio $N_s/N_t=3$, green color represents data for $N_s/N_t=4$. Solid lines correspond to data obtained using the topological susceptibility from overlap simulation and slab method, while for dashed lines we used the topological susceptibility from the staggered based results of Borsanyi:2016ksw.
• Figure 5: The spectral density of the overlap Dirac operator $\rho(\lambda/m_q)$ for the temperature $T=145$ MeV and four values of the aspect ratio $N_s/N_t=2,3,4,5$ corresponding to different panels. The temporal lattice extent is $N_t=8$. For all aspect ratios the data are for zero topological sector $Q=0$. Additionally for aspect ratio $N_s/N_t=3$ we present data in other topological sectors $=2,-4,8$.