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Register a new userFinite size scaling of meson propagators with isospin chemical potential
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Authors
G. Akemann
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We determine the volume and mass dependence of scalar and pseudoscalar two-point functions in N_f-flavour QCD, in the presence of an isospin chemical potential and at fixed gauge-field topology. We obtain these results at second order in the epsilon-expansion of Chiral Perturbation Theory and evaluate all relevant zero-mode group integrals analytically. The virtue of working with a non-vanishing chemical potential is that it provides the correlation functions with a dependence on both the chiral condensate, Sigma, and the pion decay constant, F, already at leading order. Our results may therefore be useful for improving the determination of these constants from lattice QCD calculations. As a side product, we rectify an earlier calculation of the O(epsilon^2) finite-volume correction to the decay constant appearing in the partition function. We also compute a generalised partition function which is useful for evaluating U(N_f) group integrals.
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We investigate the properties of QCD at finite isospin chemical potential at zero and non-zero temperatures. This theory is not affected by the sign problem and can be simulated using Monte-Carlo techniques. With increasing isospin chemical potential and temperatures below the deconfinement transition the system changes into a phase where charged pions condense, accompanied by an accumulation of low modes of the Dirac operator. The simulations are enabled by the introduction of a pionic source into the action, acting as an infrared regulator for the theory, and physical results are obtained by removing the regulator via an extrapolation. We present an update of our study concerning the associated phase diagram using 2+1 flavours of staggered fermions with physical quark masses and the comparison to Taylor expansion. We also present first results for our determination of the equation of state at finite isospin chemical potential and give an example for a cosmological application. The results can also be used to gain information about QCD at small baryon chemical potentials using reweighting with respect to the pionic source parameter and the chemical potential and we present first steps in this direction.
In this contribution we investigate the phase diagram of QCD in the presence of an isospin chemical potential. To alleviate the infrared problems of the theory associated with pion condensation, we introduce the pionic source as an infrared regulator. We discuss various methods to extrapolate the results to vanishing pionic source, including a novel method based on the singular value spectrum of the massive Dirac operator, a leading-order reweighting and a spline Monte-Carlo fit. Our main results concern the phase transition boundary between the normal and the pion condensation phases and the chiral/deconfinement transition temperature as a function of the chemical potential. In addition, we perform a quantitative comparison between our direct results and a Taylor-expansion obtained at zero chemical potential to assess the applicability range of the latter.
Wilson Fermions with untwisted and twisted mass are widely used in lattice simulations. Therefore one important question is whether the twist angle and the lattice spacing affect the phase diagram. We briefly report on the study of the phase diagram of QCD in the parameter space of the degenerate quark masses, isospin chemical potential, lattice spacing, and twist angle by employing chiral perturbation theory. Moreover we calculate the pion masses and their dependence on these four parameters.
We compare the low eigenvalue spectra of the Overlap Dirac operator on two sets of configurations at $mu_I/mu_I^c$ = 0.5 and 1.5 generated with dynamical staggered fermions at these isospin chemical potential on $24^3 times 6$ lattices. We find very small changes in the number of zero modes and low lying modes which is in stark contrast with those across the corresponding finite temperature phases where one sees a drop across the phase transition. Possible consequences are discussed.
Making use of the NJL model and the multiple reflection expansion pproximation, we study the phase transition of the finite size droplet with u and d quarks. We find that the dynamical masses of u, d quarks are different, and the chiral symmetry can be restored at different critical radii for u, d quark. It rovides a clue to understand the effective nucleon mass splitting in nuclear matter. Meanwhile, it shows that the maximal isospin chemical potential at zero temperature is much smaller than the mass of pion in free space.
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