Quantum chaos and QCD at finite chemical potential

A novel approach to the problem of deriving the generating functional for the canonical ensemble in lattice QCD at a nonzero chemical potential is proposed. The derivation proceeds in several steps. First, the baryon density for imaginary values of the chemical potential is obtained. Then, again for imaginary values of the chemical potential, the generating functional of the grand canonical ensemble is derived. In this analysis, a fit of baryon density is employed toward simplifying the procedure of numerical integration. Finally, the generating potential for the canonical ensemble is derived using a high-precision numerical Fourier transform. The generating functional for the canonical ensemble is also derived using the known hopping-parameter expansion, and the results obtained with the two methods are compared for the deconfinement phase in the lattice QCD with two flavors.

In this talk we present the results published recently in Ref . [1], where we showed how to introduce a quark chemical potential in the overlap Dirac operator. The resulting operator satisfies a Ginsparg-Wilson relation and has exact zero modes. It is no longer γ5-Hermitian, but its nonreal eigenvalues still occur in pairs. We compute the spectral density of the operator on the lattice and show that, for small eigenvalues, the data agree with analytical predictions of non-Hermitian chiral random matrix theory for both trivial and nontrivial topology. We also explain an observed change in the number of zero modes as a function of chemical potential.

Knowledge of the screening masses at finite chemical potential can provide insight into the nature of the QCD phase diagram. However, lattice studies at finite chemical potential suffer from the well-known issue of the sign problem, which has made the calculation of observables such as screening correlators and screening masses at finite chemical potential quite challenging. One way to proceed is by expanding the observable in a Taylor series in the chemical potential and hence calculating the finite-density corrections to the observable. In this talk, we will use this approach to calculate the screening mass of the pseudoscalar meson at finite temperatures and chemical potential by expanding the screening correlator in a Taylor series in the chemical potential. We will present our results for the second derivative of the screening mass w.r.t. the chemical potential. Our calculation was done on $64^3 \times 8$ lattices generated using the (2+1) HISQ/tree action.

We propose a new method for calculating the dressed fermionpropagator at finite chemical potential in QED3 under the rainbowapproximation of Dyson–Schwinger equation. In the aboveapproximation, we show that the dressed fermion propagator at finitechemical potential μ has the formŜ(p̃) = iγ·p̃A(p̃2) + B(p̃2)with p̃μ = (p⃗, p3 + iμ). Using thisform of fermion propagator at nonzero chemical potential, weinvestigate the Dyson–Schwinger equation for the dressed fermionpropagator at finite chemical potential and study the effectsof the chemical potential on the critical number of the fermion flavors.

QCD phase diagram in the T − μ plane and the equation of state for pure gluon, 2-flavor, 2+1-flavor systems, and 2+1+1-flavor systems have been investigated using the Einstein-Maxwell-Dilaton (EMD) framework at finite temperature and chemical potential. By inputting lattice QCD data for the equation of state and baryon number susceptibility at zero chemical potential into holographic model, all the parameters can be determined with the aid of machine learning algorithms. Our findings indicate that the deconfinement phase transition is of first order for the pure gluon system with critical temperature Tc = 0.265 GeV at vanishing chemical potential. The phase transition for the 2-flavor, 2+1-flavor systems, and 2+1+1-flavor systems are crossover at vanishing chemical potential and first-order at high chemical potential, and the critical endpoint (CEP) in the T − μ plane locates at (μBc = 0.46 GeV, Tc= 0.147 GeV), (μBc = 0.74 GeV, Tc = 0.094 GeV), and (μBc = 0.87 GeV, Tc = 0.108 GeV), respectively. Additionally, the thermodynamic quantities of the system for different flavors at finite chemical potential are presented in this paper. It is observed that the difference between the 2+1-flavor and 2+1+1-flavor systems is invisible at vanishing chemical potential and low temperature. The location of CEP for 2+1+1-flavor system deviates explicitly from that of the 2+1-flavor system with the increase of chemical potential. Both 2+1-flavor and 2+1+1-flavor systems differ significantly from the 2-flavor system. Moreover, at zero temperature, the critical chemical potential is found to be μB = 1.1 GeV, 1.6 GeV, 1.9 GeV for the 2-flavor, 2+1-flavor and 2+1+1-flavor systems, respectively.

Symmetries and spectrum of SU(2) lattice gauge theory at finite chemical potential

We update our previous results for (pseudo-)scalar mesons at zero temperature and finite quark chemical potential and generalize the investigation to include (axial-)vector mesons. We determine bound-state properties such as meson masses and decay constants up to chemical potentials far in the first-order coexistence region. To extract the bound-states properties, we solve the Bethe-Salpeter equation and utilize Landau-gauge quark and gluon propagators obtained from a coupled set of (truncated) Dyson-Schwinger equations with N_{text{ f }}=2+1 dynamical quark flavors at finite chemical potential and vanishing temperature. For multiple (pseudo-)scalar and (axial-)vector mesons, we observe constant masses and decay constants for chemical potentials up to the coexistence region of the first-order phase transition thus verifying explicitly the Silver-Blaze property of QCD. Inside the coexistence region the pion becomes more massive and its decay constants decrease, whereas corresponding quantities for the (axial-)vector mesons remain (almost) constant.

Recently it was suggested that the problem of species doubling with Kogut-Susskind lattice fermions entails, at finite chemical potential, a confusion of particles with antiparticles. What happens instead is that the familiar correspondence of positive-energy spinors to particles, and of negative-energy spinors to antiparticles, ceases to hold for the Kogut-Susskind time derivative. To show this we highlight the role of the spinorial ``energy'' in the Osterwalder-Schrader reconstruction of the Fock space of non-interacting lattice fermions at zero temperature and nonzero chemical potential. We consider Kogut-Susskind fermions and, for comparison, fermions with an asymmetric one-step time derivative.

We discuss the spectrum of the QCD Dirac operator both at zero and at nonzero baryon chemical potential. We show that, in the ergodic domain of QCD, the Dirac spectrum can be obtained from the replica limit of a Toda lattice equation. At zero chemical potential this method explains the factorization of known results into compact and noncompact integrals, and at nonzero chemical potential it allows us to derive the previously unknown microscopic spectral density.

We investigate the Gross-Neveu model on the lattice at finite temperature and chemical potential in the limit of an infinite number of fermion flavours. We check the universality of the continuum limit of staggered and overlap fermions at finite temperature and chemical potential. We show that at finite density a recently discovered phase of cold baryonic matter emerges as a baryon crystal from a spatially inhomogeneous fermion condensate. However, we also demonstrate that on the lattice, this new phase disappears at large coupling or in small volumes. Furthermore, we investigate unusual finite size effects that appear at finite chemical potential. Finally, we speculate on the implications of our findings for QCD.

In this article we study chiral symmetry breaking for quark matter in a magnetic background, B, at finite temperature and quark chemical potential, μ, making use of the Ginzburg–Landau effective action formalism. As a microscopic model to compute the effective action we use the renormalized quark–meson model in the chiral limit. Our main goal is to study the evolution of the critical endpoint, CP, as a function of the magnetic field strength, and investigate the realization of inverse magnetic catalysis at finite chemical potential. We find that the phase transition at zero chemical potential is always of the second order; for small and intermediate values of B, CP moves towards small μ, while for larger B it moves towards moderately larger values of μ. Our results are in agreement with the inverse magnetic catalysis scenario at finite chemical potential and not too large values of the magnetic field, while at larger B direct magnetic catalysis sets in.

We investigate the phase diagram of QCD with heavy quarks at finite temperature and chemical potential in the context of background field methods. In particular, we use a massive extension of the Landau-DeWitt gauge which is motivated by previous studies of the deconfinement phase transition in pure Yang-Mills theories. We show that a simple one-loop calculation is able to capture the richness of the phase diagram in the heavy quark region, both at real and imaginary chemical potential. Moreover, dimensionless ratios of quantities directly measurable in numerical simulations are in good agreement with lattice results.

The present article is the followup of Eur. Phys. J. C 79, 761 (2019), where we studied the energy loss of the heavy quarks traversing through the isotropic collisional hot QCD medium. As the QCD phase diagram at finite baryon density and the moderate temperature is expected to be traced by the upcoming experimental facilities such as Anti-proton and Ion Research (FAIR) and Nuclotron-based Ion Collider fAcility (NICA), the theoretical research needs the inclusion of finite chemical potential to study the hot QCD medium. Therefore, the aim here is to develop a formalism that investigates the collisional energy loss of heavy quarks moving in the hot QCD medium having small but a finite quark chemical potential. The calculation uses the extended effective fugacity quasi-particle model [1–3] and the effective kinetic theory with Bhatnagar-Gross-Krook (BGK) collisional kernel. The change in the energy of charm and bottom quarks with respect to their corresponding momenta has been investigated at different values of collisions frequency and chemical potential. We find that the bottom quark loses less energy than the charm quark for a fixed momentum, collisional frequency and chemical potential. The energy loss values are found to decrease with increasing chemical potential.

We discuss a novel solution for the sign problem which prevents first principle Monte-Carlo computations of QCD at finite chemical potential (especially important for both the search for the critical point and neutron star physics) as well as real time quantities such as transport coefficients. The solution is based on deforming the region of integration in the path integral into a complex manifold where the sign problem can be mitigated substantially. We explain the new Monte-Carlo algorithm based on this idea and give examples of interacting quantum field theories (bosonic and fermionic) with nonzero chemical potential as well as real time dynamics where this method successfully solves the sign problem. This approach generalizes the “Lefschetz thimble” method that received much attention lately. We also compare/contrast with the complex Langevin method.

International audience