arXiv subjects

G. Endrodi

Publications and source records attributed to G. Endrodi.

At least 19 recordsLinked to original sources

arXiv2018

Applying constrained simulations for low temperature lattice QCD at finite baryon chemical potential

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 $μ/m_N \sim 0.16 - 0.18$ on $6^4$ lattices at $β=2.9$.

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arXiv2018

QCD phase diagram for nonzero isospin-asymmetry

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 $T\approx 160$ 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.

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arXiv2017

Landau levels in 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 lowest 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.

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arXiv2016

Probing the nature of phases across the phase transition at finite isospin chemical potential

We compare the low eigenvalue spectra of the Overlap Dirac operator on two sets of configurations at $μ_I/μ_I^c$ = 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.

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arXiv2014

QCD in magnetic fields: from Hofstadter's butterfly to the phase diagram

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 - Hofstadter's butterfly - from a new, quantum field theoretical perspective. In particular, I point 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.

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arXiv2014

Magnetic structure of isospin-asymmetric QCD matter in neutron stars

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.

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arXiv2014

The QCD equation of state in background magnetic fields

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 is 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.

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arXiv2014

Local CP-violation and electric charge separation by magnetic fields from lattice QCD

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 linearly 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.

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arXiv2013

Magnetization and pressures at nonzero magnetic fields in QCD

Two approaches are pursued to determine the magnetization of the QCD vacuum at zero and nonzero temperatures using lattice simulations. The first method builds on pressure anisotropies which are induced by the magnetic field on the lattice. The second approach is a novel, generalized version of the integral method, which exploits the independence of the theory on B for asymptotically large quark masses. Both approaches give consistent results and confirm that the QCD medium is paramagnetic. Finally, an interesting relation between QCD paramagnetism, magnetic catalysis of the QCD condensate and the QED beta-function is pointed out.

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arXiv2013

Perturbative renormalization of staggered fermion operators with stout improvement: Application to the magnetic susceptibility of QCD

We calculate the fermion propagator and the quark-antiquark Green's functions for a complete set of ultralocal fermion bilinears, ${{\cal O}_Γ}$ [$Γ$: scalar (S), pseudoscalar (P), vector (V), axial (A) and tensor (T)], using perturbation theory up to one-loop and to lowest order in the lattice spacing. We employ the staggered action for fermions and the Symanzik Improved action for gluons. From our calculations we determine the renormalization functions for the quark field and for all ultralocal taste-singlet bilinear operators. The novel aspect of our calculations is that the gluon links which appear both in the fermion action and in the definition of the bilinears have been improved by applying a stout smearing procedure up to two times, iteratively. Compared to most other improved formulations of staggered fermions, the above action, as well as the HISQ action, lead to smaller taste violating effects. The renormalization functions are presented in the RI$'$ scheme; the dependence on all stout parameters, as well as on the coupling constant, the number of colors, the lattice spacing, the gauge fixing parameter and the renormalization scale, is shown explicitly. We apply our results to a nonperturbative study of the magnetic susceptibility of QCD at zero and finite temperature. In particular, we evaluate the "tensor coefficient", $τ$, which is relevant to the anomalous magnetic moment of the muon.

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arXiv2013

QCD phase diagram: overview of recent lattice results

Two parameters that have a strong influence on the finite temperature QCD transition, and play an important role in various physical scenarios are the quark density and the external magnetic field. The effect of these parameters on the thermal properties of QCD is discussed, and an overview of the latest lattice results is given.

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arXiv2013

Paramagnetic squeezing of QCD matter

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 in 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.

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arXiv2013

Inverse magnetic catalysis and the Polyakov loop

We study the physical mechanism of how an external magnetic field influences the QCD quark condensate. Two competing mechanisms are identified, both relying on the interaction between the magnetic field and the low quark modes. While the coupling to valence quarks enhances the condensate, the interaction with sea quarks suppresses it in the transition region. The latter `sea effect' acts by ordering the Polyakov loop and, thereby, reduces the number of small Dirac eigenmodes and the condensate. It is most effective around the transition temperature, where the Polyakov loop effective potential is flat and a small correction to it by the magnetic field can have a significant effect. Around the critical temperature, the sea suppression overwhelms the valence enhancement, resulting in a net suppression of the condensate, named inverse magnetic catalysis. We support this physical picture by lattice simulations including continuum extrapolated results on the Polyakov loop as a function of temperature and magnetic field. We argue that taking into account the increase in the Polyakov loop and its interaction with the low-lying modes is essential to obtain the full physical picture, and should be incorporated in effective models for the description of QCD in magnetic fields in the transition region.

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arXiv2013

Magnetic field-induced gluonic (inverse) catalysis and pressure (an)isotropy in QCD

We study the influence of strong external magnetic fields on gluonic and fermionic observables in the QCD vacuum at zero and nonzero temperatures, via lattice simulations with N_f=1+1+1 staggered quarks of physical masses. The gluonic action density is found to undergo magnetic catalysis at low temperatures and inverse magnetic catalysis near and above the transition temperature, similar to the quark condensate. Moreover, the gluonic action develops an anisotropy: the chromo-magnetic field parallel to the external field is enhanced, while the chromo-electric field in this direction is suppressed. We demonstrate that the same hierarchy is obtained using the Euler-Heisenberg effective action. Conversely, the topological charge density correlator does not reveal a significant anisotropy up to magnetic fields eB~1 GeV^2. Furthermore, we show that the pressure remains isotropic even for nonzero magnetic fields, if it is defined through a compression of the system at fixed external field. In contrast, if the flux of the field is kept fixed during the compression -- which is the situation realized in the lattice simulation -- the pressure develops an anisotropy. We estimate the quark and gluonic contributions to this anisotropy, and relate them to the magnetization of the QCD vacuum. After performing electric charge renormalization, we obtain an estimate for the magnetization, which indicates that QCD is paramagnetic.

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arXiv2013

Thermodynamic properties of QCD in external magnetic fields

We consider the effect of strong external electromagnetic fields on thermodynamic observables in QCD, through lattice simulations with 1+1+1 flavors of staggered quarks at physical quark masses. Continuum extrapolated results are presented for the light quark condensates and for their tensor polarizations, as functions of the temperature and the magnetic field. We find the light condensates to undergo inverse magnetic catalysis in the transition region, in a manner that the transition temperature decreases with growing magnetic field. We also compare the results to other approaches and lattice simulations. Furthermore, we relate the tensor polarization to the spin part of the magnetic susceptibility of the QCD vacuum, and show that this contribution is diamagnetic.

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arXiv2012

Magnetic susceptibility of QCD at zero and at finite temperature from the lattice

The response of the QCD vacuum to a constant external (electro)magnetic field is studied through the tensor polarization of the chiral condensate and the magnetic susceptibility at zero and at finite temperature. We determine these quantities using lattice configurations generated with the tree-level Symanzik improved gauge action and N_f=1+1+1 flavors of stout smeared staggered quarks with physical masses. We carry out the renormalization of the observables under study and perform the continuum limit both at T>0 and at T=0, using different lattice spacings. Finite size effects are studied by using various spatial lattice volumes. The magnetic susceptibilities χ_f reveal a diamagnetic behavior; we obtain at zero temperature χ_u=-(2.08 +/- 0.08) 1/GeV^2, χ_d=-(2.02 +/- 0.09) 1/GeV^2 and χ_s=-(3.4 +/- 1.4) 1/GeV^2 for the up, down and strange quarks, respectively, in the MSBar scheme at a renormalization scale of 2 GeV. We also find the polarization to change smoothly with the temperature in the confinement phase and then to drastically reduce around the transition region.

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arXiv2012

QCD quark condensate in external magnetic fields

We present a comprehensive analysis of the light condensates in QCD with 1+1+1 sea quark flavors (with mass-degenerate light quarks of different electric charges) at zero and nonzero temperatures of up to 190 MeV and external magnetic fields B<1 GeV^2/e. We employ stout smeared staggered fermions with physical quark masses and extrapolate the results to the continuum limit. At low temperatures we confirm the magnetic catalysis scenario predicted by many model calculations, while around the crossover the condensate develops a complex dependence on the external magnetic field, resulting in a decrease of the transition temperature.

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arXiv2012

QCD equation of state at nonzero chemical potential: continuum results with physical quark masses at order mu^2

We determine the equation of state of QCD for nonzero chemical potentials via a Taylor expansion of the pressure. The results are obtained for N_f=2+1 flavors of quarks with physical masses, on various lattice spacings. We present results for the pressure, interaction measure, energy density, entropy density, and the speed of sound for small chemical potentials. At low temperatures we compare our results with the Hadron Resonance Gas model. We also express our observables along trajectories of constant entropy over particle number. A simple parameterization is given (the Matlab/Octave script parameterization.m, submitted to the arXiv along with the paper), which can be used to reconstruct the observables as functions of T and mu, or as functions of T and S/N.

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