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We consider bosonic random matrix partition functions at nonzero chemical potential and compare the chiral condensate, the baryon number density and the baryon number susceptibility to the result of the corresponding fermionic partition function. We find that as long as results are finite, the phase transition of the fermionic theory persists in the bosonic theory. However, in case that bosonic partition function diverges and has to be regularized, the phase transition of the fermionic theory does not occur in the bosonic theory, and the bosonic theory is always in the broken phase.
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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 $Z_n(T)$ are coefficients of this expansion. Using various methods we study properties of $Z_n(T)$. At the last step we perform cubic spline for temperature dependence of $Z_n(T)$ at fixed $n$ and compute baryon number susceptibility $chi_B/T^2$ as function of temperature. After that we compute numerically $partialchi/ partial T$ and restore crossover line in QCD phase diagram. We use improved Wilson fermions and Iwasaki gauge action on the $16^3 times 4$ lattice with $m_{pi}/m_{rho} = 0.8$ as a sandbox to check the canonical approach. In this framework we obtain coefficient in parametrization of crossover line $T_c(mu_B^2)=T_cleft(c-kappa, mu_B^2/T_c^2right)$ with $kappa = -0.0453 pm 0.0099$.
Lattice QCD at finite chemical potential is difficult due to the sign problem. We use stochastic quantization and complex Langevin dynamics to study this issue. First results for QCD in the hopping expansion are encouraging. U(1) and SU(3) one link models are used to gain further insight into why the method appears to be successful.
The behavior of quenched Dirac spectra of two-dimensional lattice QCD is consistent with spontaneous chiral symmetry breaking which is forbidden according to the Coleman-Mermin-Wagner theorem. One possible resolution of this paradox is that, because of the bosonic determinant in the partially quenched partition function, the conditions of this theorem are violated allowing for spontaneous symmetry breaking in two dimensions or less. This goes back to work by Niedermaier and Seiler on nonamenable symmetries of the hyperbolic spin chain and earlier work by two of the auhtors on bosonic partition functions at nonzero chemical potential. In this talk we discuss chiral symmetry breaking for the bosonic partition function of QCD at nonzero isospin chemical potential and a bosonic random matrix theory at imaginary chemical potential and compare the results with the fermionic counterpart. In both cases the chiral symmetry group of the bosonic partition function is noncompact.
Partition functions of two different matrix models for QCD with chemical potential are computed for an arbitrary number of quark and complex conjugate anti-quark flavors. In the large-N limit of weak nonhermiticity complete agreement is found between the two models. This supports the universality of such fermionic partition functions, that is of products of characteristic polynomials in the complex plane. In the strong nonhermiticity limit agreement is found for an equal number of quark and conjugate flavours. For a general flavor content the equality of partition functions holds only for small chemical potential. The chiral phase transition is analyzed for an arbitrary number of quarks, where the free energy presents a discontinuity of first order at a critical chemical potential. In the case of nondegenerate flavors there is first order phase transition for each separate mass scale.
We investigate chemical-potential ($mu$) dependence of the static-quark free energies in both the real and imaginary $mu$ regions, using the clover-improved two-flavor Wilson fermion action and the renormalization-group improved Iwasaki gauge action. Static-quark potentials are evaluated from Polyakov-loop correlators in the deconfinement phase and the imaginary $mu=imu_{rm I}$ region and extrapolated to the real $mu$ region with analytic continuation. As the analytic continuation, the potential calculated at imaginary $mu=imu_{rm I}$ is expanded into a Taylor-expansion series of $imu_{rm I}/T$ up to 4th order and the pure imaginary variable $imu_{rm I}/T$ is replaced by the real one $mu_{rm R}/T$. At real $mu$, the 4th-order term weakens $mu$ dependence of the potential sizably. Also, the color-Debye screening mass is extracted from the color-singlet potential at imaginary $mu$, and the mass is extrapolated to real $mu$ by analytic continuation. The screening mass thus obtained has stronger $mu$ dependence than the prediction of the leading-order thermal perturbation theory at both real and imaginary $mu$.
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