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Register a new userThe QCD phase transition with physical-mass, chiral quarks
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We report on the first lattice calculation of the QCD phase transition using chiral fermions at physical values of the quark masses. This calculation uses 2+1 quark flavors, spatial volumes between (4 fm$)^3$ and (11 fm$)^3$ and temperatures between 139 and 196 MeV . Each temperature was calculated using a single lattice spacing corresponding to a temporal Euclidean extent of $N_t=8$. The disconnected chiral susceptibility, $chi_{rm disc}$ shows a pronounced peak whose position and height depend sensitively on the quark mass. We find no metastability in the region of the peak and a peak height which does not change when a 5 fm spatial extent is increased to 10 fm. Each result is strong evidence that the QCD ``phase transition is not first order but a continuous cross-over for $m_pi=135$ MeV. The peak location determines a pseudo-critical temperature $T_c = 155(1)(8)$ MeV. Chiral $SU(2)_Ltimes SU(2)_R$ symmetry is fully restored above 164 MeV, but anomalous $U(1)_A$ symmetry breaking is non-zero above $T_c$ and vanishes as $T$ is increased to 196 MeV.
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Chiral Random Matrix Theory has proven to describe the spectral properties of low temperature QCD very well. However, at temperatures above the chiral symmetry restoring transition it can not provide a global description. The level-spacing distribution in the lower part of the spectrum of the Dirac operator is Poisson-like. There the eigenmodes are localized in space-time and separated from the rest of the spectrum by a so-called mobility edge. In analogy to Anderson localization in condensed-matter systems with random disorder this has been called the QCD-Anderson transition. Here, we study the localization features of the low-lying eigenmodes of the massless overlap operator on configurations generated with $N_f=2+1+1$ twisted mass Wilson sea quarks and present results concerning the temperature dependence of the mobility edge and the mechanism of the quark-mode localization. We have used various methods to fix the spectral position of the delocalization transition and verify that the mobility edge extrapolates to zero at a temperature within the chiral transition region.
We present a lattice QCD based determination of the chiral phase transition temperature in QCD with two degenerate, massless quarks and a physical strange quark mass. We propose and calculate two novel estimators for the chiral transition temperature for several values of the light quark masses, corresponding to Goldstone pion masses in the range of $58~{rm MeV}lesssim m_pilesssim 163~{rm MeV}$. The chiral phase transition temperature is determined by extrapolating to vanishing pion mass using universal scaling analysis. Finite volume effects are controlled by extrapolating to the thermodynamic limit using spatial lattice extents in the range of $2.8$-$4.5$ times the inverse of the pion mass. Continuum extrapolations are carried out by using three different values of the lattice cut-off, corresponding to lattices with temporal extent $N_tau=6, 8$ and $12$. After thermodynamic, continuum and chiral extrapolations we find the chiral phase transition temperature $T_c^0=132^{+3}_{-6}$ MeV.
We investigate the nature of the chiral phase transition in the massless two-flavor QCD using the renormalization group improved gauge action and the Wilson quark action on $32^3times 16$, $24^3times 12$, and $16^3times 8$ lattices. We calculate the spacial and temporal propagators of the iso-triplet mesons in the pseudo-scalar ($PS$), scalar ($S$), vector ($V$) and axial-vector ($AV$) channels on the lattice of three sizes. We first verify that the RG scaling is excellently satisfied for all cases. This is consistent with the claim that the chiral phase transition is second order. Then we compare the spacial and temporal effective masses between the axial partners, i.e. $PS$ vs $S$ and $V$ vs $AV$, on each of the three size lattices. We find the effective masses of all of six cases for the axial partners agree remarkably. This is consistent with the claim that at least $Z_4$ subgroup of the $U_A(1)$ symmetry in addition to the $SU_A(2)$ symmetry is recovered at the chiral phase transition point.
Attempts to extract the order of the chiral transition of QCD at zero chemical potential, with two dynamical flavors of massless quarks, from simulations with progressively decreasing pion mass have remained inconclusive because of their increasing numerical cost. In an alternative approach to this problem, we consider the path integral as a function of continuous number $N_text{f}$ of degenerate quarks. If the transition in the chiral limit is first-order for $N_text{f} ge 3$, a second-order transition for $N_text{f}=2$ then requires a tricritical point in between. This in turn implies tricritical scaling of the critical boundary line between the first-order and crossover regions as the chiral limit is approached. Non-integer numbers of fermion flavors are easily implemented within the staggered fermion discretization. Exploratory simulations at $mu=0$ and $N_text{f} = 2.8, 2.6, 2.4, 2.2, 2.1$, on coarse $N_tau = 4$ lattices, indeed show a smooth variation of the critical mass mapping out a critical line in the $(m,N_text{f})$-plane. For the smallest masses the line appears consistent with tricritical scaling, allowing for an extrapolation to the chiral limit.
We present simulation results for lattice QCD with chiral fermions in small volumes, where the epsilon-expansion of chiral perturbation theory applies. Our data for the low lying Dirac eigenvalues, as well as mesonic correlation functions, are in agreement with analytical predictions. This allows us to extract values for the leading Low Energy Constants F_{pi} and Sigma.
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