Giuseppe Di Carlo

Finite density QCD: a new approach

We introduce a new approach to analyze the phase diagram of QCD at finite chemical potential and temperature, test it in the Gross-Neveu model at finite baryon density, and apply it to the study of the chemical potential-temperature phase diagram of QCD with four degenerate flavors of Kogut-Susskind type.

Phase diagram of QCD with four quark flavors at finite temperature and baryon density

Abstract We analyze the phase diagram of QCD with four staggered flavors in the ( μ , T ) plane using a method recently proposed by us. We explore the region T ≳ 0.7 T C and μ ≲ 1.4 T C , where T C is the transition temperature at zero baryon density, and find a first order transition line. Our results are quantitatively compatible with those obtained with the imaginary chemical potential approach and the double reweighting method, in the region where these approaches are reliable, T ≳ 0.9 T C and μ ≲ T C . But, in addition, our method allows us to extend the transition line to lower temperatures and higher chemical potentials.

Diquark condensation at strong coupling

The possibility of diquark condensation at sufficiently large baryon chemical potential and zero temperature is analyzed in QCD at strong coupling. In agreement with other strong coupling analysis, it is found that a first order phase transition separates a low density phase with chiral symmetry spontaneously broken from a high density phase where chiral symmetry is restored. In none of the phases diquark condensation takes place as an equilibrium state, but, for any value of the chemical potential, there is a metastable state characterized by a non-vanishing diquark condensate. The energy difference between this metastable state and the equilibrium state decreases with the chemical potential and is minimum in the high density phase. The results indicate that there is attraction in the quark-quark sector also at strong coupling, and that the attraction is more effective at high baryon density, but for infinite coupling it is not enough to produce diquark condensation. It is argued that the absence of diquark condensation is not a peculiarity of the strong coupling limit, but persists at sufficiently large finite couplings.

Critical behavior of CP(1) at theta=pi, Haldane's conjecture, and the relevant universality class.

Using an approach to analyze the theta dependence of systems with a theta term we recently proposed, the critical behavior of CP(10 at theta=pi is studied. We find a region outside the strong coupling regime where Haldanes conjecture is verified. The critical line, however, does not belong to the universality class of the Wess-Zumino-Novikov-Witten model at topological coupling k=1 since it shows continuously varying critical exponents.

Critical behaviour of the O(3) nonlinear sigma model with topological term at theta=pi from numerical simulations

We investigate the critical behaviour at theta=pi of the two-dimensional O(3) nonlinear sigma model with topological term on the lattice. Our method is based on numerical simulations at imaginary values of theta, and on scaling transformations that allow a controlled analytic continuation to real values of theta. Our results are compatible with a second order phase transition, with the critical exponent of the SU(2)_1 Wess-Zumino-Novikov-Witten model, for sufficiently small values of the coupling.

Elucidating the vacuum structure of the Aoki phase

In this paper, we discuss the vacuum structure of QCD with two flavors of Wilson fermions, inside the Aoki phase. We provide numerical evidence, coming from HMC simulations in 44, 64 and 84 lattices, supporting a vacuum structure for this model at strong coupling more complex than the one assumed in the standard wisdom, with new vacua where the expectation value of iψ¯γ5ψ can take non-zero values, and which can not be connected with the Aoki vacua by parity–flavor symmetry transformations.

Spectral Flow and Index Theorem for Staggered Fermions

We investigate numerically the spectral flow introduced by Adams for the staggered Dirac operator on realistic gauge configurations. We study both the unimproved and the HISQ Dirac operators. We compare the spectral flow index with the index obtained by identifying low-lying modes of large chirality.

Larger physical volume with a noncompact lattice regularization of SU(N) theories

Abstract Recently it has been found that in a noncompact formulation of the SU(2) gauge theory on a lattice the physical volume is larger than in the Wilson theory with the same number of sites. In its original formulation such noncompact regularization is directly applicable to U(N) theories for any N and to SU(N) theories for N=2 only. In this work we extend it to SU(N) for any N and investigate some of its properties.

Antiferromagnetic Ising model in an imaginary magnetic field

We study the two-dimensional antiferromagnetic Ising model with a purely imaginary magnetic field, which can be thought of as a toy model for the usual θ physics. Our motivation is to have a benchmark calculation in a system which suffers from a strong sign problem, so that our results can be used to test Monte Carlo methods developed to tackle such problems. We analyze here this model by means of analytical techniques, computing exactly the first eight cumulants of the expansion of the effective Hamiltonian in powers of the inverse temperature, and calculating physical observables for a large number of degrees of freedom with the help of standard multiprecision algorithms. We report accurate results for the free energy density, internal energy, standard and staggered magnetization, and the position and nature of the critical line, which confirm the mean-field qualitative picture, and which should be quantitatively reliable, at least in the high-temperature regime, including the entire critical line.

Symmetries and vacuum structure inside the Aoki phase

After performing an analysis of the complete P.D.F. (probab ility distribution function) of several interesting operators inside the Aoki phase, we find str ong indications that the P′ symmetry (combination of Parity and a discrete flavor transformation ) which forcesiψ̄γ5ψ to be zero, is spontaneously broken. This result suggests a more complica ted v cuum structure for the Aoki phase,contradicting the original χPT predictions.