We study the density of states method as well as reweighting to explore the low temperature phase diagram of QCD at finite baryon chemical potential. We use four flavors of staggered quarks, a tree-level Symanzik improved gauge action and four stout
smearing steps on lattices with $N_s=4,6,8$ and $N_t=6 - 16$. We compare our results to that of the phase quenched ensemble and also determine the pion and nucleon masses. In the density of states approach we applied pion condensate or gauge action density fixing. We found that the density of states method performs similarly to reweighting. At $T approx 100$ MeV, we found an indication of the onset of the quark number density at around $mu/m_N sim 0.16 - 0.18$ on $6^4$ lattices at $beta=2.9$.
The QCD phase diagram is studied in the presence of an isospin asymmetry using continuum extrapolated staggered quarks with physical masses. In particular, we investigate the phase boundary between the normal and the pion condensation phases and the
chiral/deconfinement transition. The simulations are performed with a small explicit breaking parameter in order to avoid the accumulation of zero modes and thereby stabilize the algorithm. The limit of vanishing explicit breaking is obtained by means of an extrapolation, which is facilitated by a novel improvement program employing the singular value representation of the Dirac operator. Our findings indicate that no pion condensation takes place above $Tapprox 160$ MeV and also suggest that the deconfinement crossover continuously connects to the BEC-BCS crossover at high isospin asymmetries. The results may be directly compared to effective theories and model approaches to QCD.
We present first evidence for the Landau level structure of Dirac eigenmodes in full QCD for nonzero background magnetic fields, based on first principles lattice simulations using staggered quarks. Our approach involves the identification of the low
est Landau level modes in two dimensions, where topological arguments ensure a clear separation of these modes from energetically higher states, and an expansion of the full four-dimensional modes in the basis of these two-dimensional states. We evaluate various fermionic observables including the quark condensate and the spin polarization in this basis to find how much the lowest Landau level contributes to them. The results allow for a deeper insight into the dynamics of quarks and gluons in background magnetic fields and may be directly compared to low-energy models of QCD employing the lowest Landau level approximation.
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.
I revisit the problem of a charged particle on a two-dimensional lattice immersed in a constant (electro)magnetic field, and discuss the energy spectrum - Hofstadters butterfly - from a new, quantum field theoretical perspective. In particular, I poi
nt out that there is an intricate interplay between a) the structure of the butterfly at low magnetic flux, b) the absence of asymptotic freedom in QED and c) the enhancement of the quark condensate by a magnetic field at zero temperature. I proceed to discuss the response of the QCD condensate to the magnetic field at nonzero temperatures in four space-time dimensions, present the resulting phase diagram and compare it to low-energy model predictions.
We study QCD under the influence of background magnetic fields and isospin chemical potentials using lattice simulations. This setup exhibits a sign problem which is circumvented using a Taylor-expansion in the magnetic field. The ground state of the
system in the pion condensation phase is found to exhibit a pronounced diamagnetic response. We elaborate on how this diamagnetism may contribute to the pressure balance in the inner core of strongly magnetized neutron stars. In addition we show that the onset of pion condensation shifts to larger chemical potentials due to the enhancement of the charged pion mass for growing magnetic fields. Finally, we sketch the magnetic structure of the QCD phase diagram in the temperature-isospin chemical potential plane.
We determine the equation of state of 2+1-flavor QCD with physical quark masses, in the presence of a constant (electro)magnetic background field on the lattice. To determine the free energy at nonzero magnetic fields we develop a new method, which i
s based on an integral over the quark masses up to asymptotically large values where the effect of the magnetic field can be neglected. The method is compared to other approaches in the literature and found to be advantageous for the determination of the equation of state up to large magnetic fields. Thermodynamic observables including the longitudinal and transverse pressure, magnetization, energy density, entropy density and interaction measure are presented for a wide range of temperatures and magnetic fields, and provided in ancillary files. The behavior of these observables confirms our previous result that the transition temperature is reduced by the magnetic field. We calculate the magnetic susceptibility and permeability, verifying that the thermal QCD medium is paramagnetic around and above the transition temperature, while we also find evidence for weak diamagnetism at low temperatures.
We study local CP-violation on the lattice by measuring the local correlation between the topological charge density and the electric dipole moment of quarks, induced by a constant external magnetic field. This correlator is found to increase linearl
y with the external field, with the coefficient of proportionality depending only weakly on temperature. Results are obtained on lattices with various spacings, and are extrapolated to the continuum limit after the renormalization of the observables is carried out. This renormalization utilizes the gradient flow for the quark and gluon fields. Our findings suggest that the strength of local CP-violation in QCD with physical quark masses is about an order of magnitude smaller than a model prediction based on nearly massless quarks in domains of constant gluon backgrounds with topological charge. We also show numerical evidence that the observed local CP-violation correlates with spatially extended electric dipole structures in the QCD vacuum.
We determine the magnetization of Quantum Chromodynamics (QCD) for several temperatures around and above the transition between the hadronic and the quark-gluon phases of strongly interacting matter. We obtain a paramagnetic response that increases i
n strength with the temperature. We argue that due to this paramagnetism, chunks of quark-gluon plasma produced in non-central heavy ion collisions should become elongated along the direction of the magnetic field. This anisotropy will then contribute to the elliptic flow v_2 observed in such collisions, in addition to the pressure gradient that is usually taken into account. We present a simple estimate for the magnitude of this new effect and a rough comparison to the effect due to the initial collision geometry. We conclude that the paramagnetic effect might have a significant impact on the value of v_2.
We determine the phase diagram of QCD on the mu-T plane for small to moderate chemical potentials. Two transition lines are defined with two quantities, the chiral condensate and the strange quark number susceptibility. The calculations are carried o
ut on N_t =6,8 and 10 lattices generated with a Symanzik improved gauge and stout-link improved 2+1 flavor staggered fermion action using physical quark masses. After carrying out the continuum extrapolation we find that both quantities result in a similar curvature of the transition line. Furthermore, our results indicate that in leading order the width of the transition region remains essentially the same as the chemical potential is increased.
