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Register a new userFinite density QCD phase transition in the heavy quark region
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We extend our previous study of the QCD phase structure in the heavy quark region to non-zero chemical potentials. To identify the critical point where the first order deconfining transition terminates, we study an effective potential defined by the probability distribution function of the plaquette and the Polyakov loop. The reweighting technique is shown to be powerful in evaluating the effective potential in a wide range of the plaquette and Polyakov loop expectation values. We adopt the cumulant expansion to overcome the sign problem in the calculation of complex phase of the quark determinant. We find that the method provides us with an intuitive and powerful way to study the phase structure. We estimate the location of the critical point at finite chemical potential in the heavy quark region.
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We study the phase structure of lattice QCD with heavy quarks at finite temperature and density by a histogram method. We determine the location of the critical point at which the first-order deconfining transition in the heavy-quark limit turns into a crossover at intermediate quark masses through a change of the shape of the histogram under variation of coupling parameters. We estimate the effect of the complex phase factor which causes the sign problem at finite density, and show that, in heavy-quark QCD, the effect is small around the critical point. We determine the critical surface in 2+1 flavor QCD in the heavy-quark region at all values of the chemical potential mu including mu=infty.
We study the end point of the first-order deconfinement phase transition in two and 2+1 flavor QCD in the heavy quark region of the quark mass parameter space. We determine the location of critical point at which the first-order deconfinement phase transition changes to crossover, and calculate the pseudo-scalar meson mass at the critical point. Performing quenched QCD simulations on lattices with the temporal extents Nt=6 and 8, the effects of heavy quarks are determined using the reweighting method. We adopt the hopping parameter expansion to evaluate the quark determinants in the reweighting factor. We estimate the truncation error of the hopping parameter expansion by comparing the results of leading and next-to-leading order calculations, and study the lattice spacing dependence as well as the spatial volume dependence of the result for the critical point. The overlap problem of the reweighting method is also examined. Our results for Nt=4 and 6 suggest that the critical quark mass decreases as the lattice spacing decreases and increases as the spatial volume increases.
We study the endpoint of the first order deconfinement phase transition of 2 and 2+1 flavor QCD in the heavy quark region. We perform simulations of quenched QCD and apply the reweighting method to study the heavy quark region. The quark determinant for the reweighting is evaluated by a hopping parameter expansion. To reduce the overlap problem, we introduce an external source term of the Polyakov loop in the simulation. We study the location of critical point at which the first order phase transition changes to crossover by investigating the histogram of the Polyakov loop and applying the finite-size scaling analysis. We estimate the truncation error of the hopping parameter expansion, and discuss the lattice spacing dependence and the spatial volume dependence in the result of the critical point.
Finite-size scaling is investigated in detail around the critical point in the heavy-quark region of nonzero temperature QCD. Numerical simulations are performed with large spatial volumes up to the aspect ratio $N_s/N_t=12$ at a fixed lattice spacing with $N_t=4$. We show that the Binder cumulant and the distribution function of the Polyakov loop follow the finite-size scaling in the $Z(2)$ universality class for large spatial volumes with $N_s/N_t ge 9$, while, for $N_s/N_t le 8$, the Binder cumulant becomes inconsistent with the $Z(2)$ scaling. To realize the large-volume simulations in the heavy-quark region, we adopt the hopping tails expansion for the quark determinant: We generate gauge configurations using the leading order action including the Polyakov loop term for $N_t=4$, and incorporate the next-to-leading order effects in the measurements by the multipoint reweighting method. We find that the use of the leading-order configurations is crucially effective in suppressing the overlapping problem in the reweighting and thus reducing the statistical errors.
Complex nature of finite density QCD with heavy quarks in the strong coupling region is studied. For this purpose, we consider the effective potential as a function of Polyakov line, and study thermodynamic singularities and associated Stokes boundaries in the complex chemical potential plane. We also perform an explicit analytic continuation of the first order transition and crossover lines in the complex chemical potential plane.
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