Abstract
Using GPGPU techniques and multi-precision calculation we developed the code to study QCD phase transition line in the canonical approach. The canonical approach is a powerful tool to investigate sign problem in Lattice QCD. The central part of the canonical approach is the fugacity expansion of the grand canonical partition functions. Canonical partition functions Zn(T) are coefficients of this expansion. Using various methods we study properties of Zn(T). At the last step we perform cubic spline for temperature dependence of Zn(T) at fixed n and compute baryon number susceptibility χB/T2 as function of temperature. After that we compute numerically ∂χ/∂T and restore crossover line in QCD phase diagram. We use improved Wilson fermions and Iwasaki gauge action on the 163 × 4 lattice with mπ/mρ = 0.8 as a sandbox to check the canonical approach. In this framework we obtain coefficient in parametrization of crossover line Tc(µ2B) = Tc(C−ĸµ2B/T2c) with ĸ = −0.0453 ± 0.0099.
Highlights
A lattice QCD simulation is a first-principles calculation, and this makes it possible to study the quark/hadron world using a non-perturbative approach
In this letter we presented evidence that the canonical approach can be useful to study QCD matter at non zero baryon chemical potential
We believe that canonical approach is one of the most promising approaches to study strong interacting matter from the first principles
Summary
A lattice QCD simulation is a first-principles calculation, and this makes it possible to study the quark/hadron world using a non-perturbative approach. Where μ is the chemical potential, T is the temperature, His the Hamiltonian, Nis the quark number operator, det ∆(μ) is the fermion determinant, and S G is the gluon field action. When μ takes a nonzero real value, the fermion determinant becomes a complex number. This is problematic, because in the Monte Carlo simulations, we generate the gluon fields with the probability. In Eq (3), canonical partition functions Zn do not depend on μ, and Eq (3) works for real, imaginary, and even complex μ. When the chemical potential is pure imaginary, μ = iμI, the fermion determinant is real, and in those regions, we can construct Zn from ZG. After determining Zn in this way, we can study real physical μ regions using formula (3)
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