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V. G. Bornyakov

Publications and source records attributed to V. G. Bornyakov.

At least 19 recordsLinked to original sources
arXiv2025

Decomposition of the static potential in SU(3) gluodynamics

After fixing the Maximal Abelian gauge in SU(3) lattice gluodynamics we decompose the nonabelian gauge field into the Abelian field created by Abelian monopoles and the modified nonabelian field with monopoles removed. We then calculate respective static potentials in the fundamental representation and show that the sum of these potentials approximates the nonabelian static potential with good precision at all distances considered. Comparison with other ways of decomposition is made.

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arXiv2024

Quark Density in Lattice QC$_2$D at Imaginary and Real Chemical Potential

We study lattice two-color QCD (QC$_2$D) with two flavors of staggered fermions at imaginary and real quark chemical potential $μ_q$ and $T>T_c$. We employ various methods of extrapolation of the quark number density from imaginary to real quark chemical potentials $μ_q$, including series expansions as well as analytic continuation based on phenomenological models, and study their accuracy by comparing the results to the lattice data. Below the Roberge-Weiss temperature, $T T_{RW}$ we show that the analytic continuation to the real values of $μ_q$ based on trigonometric functions works equally well with the conventional method based on the Taylor expansion in powers of $μ_q$.

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arXiv2024

Gribov copy effects in the maximal Abelian gauge

We study effects of Gribov copies in the Maximal Abelian gauge in $SU(3)$ lattice gluodynamics. We confirm earlier results that with effective gauge fixing algorithm one finds Gribov copies of the maximal Abelian gauge which produce about 90\% of the nonabelian string tension after Abelian projection. At the same time using much less effective relaxation algorithm one finds Gribov copies with nice Abelian dominance for the string tension.

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arXiv2023

Studies of Correlations in the Critical Domain of the $SU(2)$ Gluodynamics

By considering the example of $SU(2)$ gluodynamics, we check numerically the idea that the strong correlation of the Polyakov loop with the longitudinal gluon propagator and related quantities can be used to substantially reduce the finite-volume effects as well as to extrapolate in temperature over the critical domain.

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arXiv2022

Numerical Study of the Roberge-Weiss Transition

We study the Roberge-Weiss phase transition numerically. The phase transition is associated with the discontinuities in the quark-number density at specific values of imaginary quark chemical potential. We parameterize the quark number density $ρ_q$ by the polynomial fit function to compute the canonical partition functions. We demonstrate that this approach provides a good framework for analyzing lattice QCD data at finite density and a high temperature. We show numerically that at high temperature, the Lee-Yang zeros lie on the negative real semi-axis provided that the high-quark-number contributions to the grand canonical partition function are taken into account. These Lee-Yang zeros have nonzero linear density, which signals the Roberge-Weiss phase transition. We demonstrate that this density agrees with the quark density discontinuity at the transition line.

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arXiv2022

Study of two color QCD on large lattices

We study two colors lattice QCD (QC$_2$D) with two flavors of staggered fermions on $40^4$ and $32^4$ lattices with lattice spacing $a =0.048$~fm in the wide range of the quark chemical potential $μ_q$. Our focus is on the confinement-deconfinement transition in this theory. Thus we compute the string tension from the Wilson loops and the static quark free energy from the Polyakov loops. We find that the deconfinement transition found earlier in the range $μ_q \approx 800 - 1000$ MeV is shifted to higher values. This shift is attributed to decreasing of the lattice spacing used in our simulations in comparison with the earlier study.

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arXiv2022

The Difference between the Longitudinal and Transverse Gluon Propagators as an Indicator of the Postconfinement Domain

We study numerically the dependence of the difference between the longitudinal and transverse gluon propagators, $Δ=D_L-D_T$, on the momentum and temperature at $T\gtrsim T_c$ both in SU(2) and SU(3) gluodynamics. It is found that the integral of $Δ$ with respect to the 3-momentum is sensitive only to infrared dynamics and shows a substantial correlation with the Polyakov loop. At $T=T_p\sim 1.2 T_c$ it changes sign giving some evidence that $T_p$ can serve as a boundary of the postconfinement domain.

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arXiv2022

Correlations and Critical Behavior in Lattice Gluodynamics

In the Landau-gauge lattice gluodynamics we find that, both in the SU(2) and SU(3) theory, a correlation of the Polyakov loop with the asymmetry of the $A^2$ gluon condensate as well as with the longitudinal propagator makes it possible to determine the critical behavior of these quantities. We discuss finite-volume corrections and reveal that they can be reduced by the use of regression analysis. We also analyze the temperature dependence of low-momenta propagators in different Polyakov-loop sectors.

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arXiv2021

Gluon Propagators in $2+1$ Lattice QCD with Nonzero Isospin Chemical Potential

The static longitudinal and transverse gluon propagators in the Landau gauge are studied in $2+1$ lattice QCD with nonzero isospin chemical potential $μ_I$. Parameterization of the momentum dependence of the propagators is provided for all values of the chemical potential under study. We find that the longitudinal propagator is infrared suppressed at nonzero $μ_I$ with suppression increasing with increasing $μ_I$. It is found, respectively, that the electric screening mass is increasing with increasing $μ_I$. Additionally, we analyze the difference between two propagators as a function of the momentum and thus compare interactions in chromoelectric and chromomagnetic sectors.

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arXiv2021

Decomposition of the SU(2) gauge field in the Maximal Abelian gauge

We study decomposition of $SU(2)$ gauge field into monopole and monopoleless components. After fixing the Maximal Abelian gauge in $SU(2)$ lattice gauge theory we decompose the nonabelian gauge field into the Abelian field created by monopoles and the modified nonabelian field with monopoles removed. We then calculate respective static potentialis and show that the potential due to the modified nonabelian field is nonconfining while, as is well known, the Abelian field produces linear potential. We further find that the sum of these potentials approximates the nonabelian static potential with good precision at all distances considered. We conclude that at large distances the monopole field potential describes the classical energy of the hadronic string while the static potential due to the modified nonabelian field describes the string fluctuations energy.

hep-lat↗
arXiv2021

The $A^2$ Asymmetry and Gluon Propagators in Lattice $SU(3)$ Gluodynamics at $T\simeq T_c$

We study numerically the chromoelectric-chromomagnetic asymmetry of the dimension two $A^2$ gluon condensate as well as the infrared behavior of the gluon propagators at $T\simeq T_c$ in the Landau-gauge $SU(3)$ lattice gauge theory. We find that a very significant correlation of the real part of the Polyakov loop with the asymmetry as well as with the longitudinal propagator makes it possible to determine the critical behavior of these quantities. We obtain the screening masses in different Polyakov-loop sectors and discuss the dependence of chromoelectric and chromomagnetic interactions of static color charges and currents on the choice of the Polyakov-loop sector in the deconfinement phase.

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arXiv2021

Gluons in Two-Color QCD at High Baryon Density

Landau gauge longitudinal and transverse gluon propagators are studied in lattice QCD with gauge group $SU(2)$ at varying temperature and quark density. In particular, it is found that the longitudinal propagator decreases with increasing quark chemical potential at all temperatures under study, whereas the transverse propagator increases with increasing quark chemical potential at $T<200$ MeV and does not depend on it at higher temperatures. The relative strength of chromoelectric and chromomagnetic interactions is also discussed.

hep-lat↗
arXiv2020

Effects of Dense Quark Matter on Gluon Propagators in Lattice QC$_2$D

The transverse and longitudinal gluon propagators in the Landau gauge are studied in the two-color lattice QCD at nonzero quark chemical potential $μ_q$. Parameterization of the momentum dependence of the propagators is provided for all values of chemical potential under study. We find that the longitudinal propagator is infrared suppressed at nonzero $μ_q$ with suppression increasing with increasing $μ_q$. The transverse propagator dependence on $μ_q$ was found to be opposite: it is enhanced at large $μ_q$. It is found, respectively, that the electric screening mass is increasing while the magnetic screening mass is decreasing with increasing $μ_q$. Nice agreement between the electric screening mass computed from the longitudinal propagator and the Debye mass computed earlier from the singlet static quark-antiquark potential was found. We discuss how the dependence of the propagators on the chemical potential correlates with the respective dependence of the string tension. Additionally, we consider the difference between two propagators as a function of the momentum and make interesting observations.

hep-lat↗
arXiv2019

Lattice study of static quark-antiquark interactions in dense quark matter

In this paper we study the interactions among a static quark-antiquark pair in the presence of dense two-color quark matter with lattice simulation. To this end we compute Polyakov line correlation functions and determine the renormalized color averaged, color singlet and color triplet grand potentials. The color singlet grand potential allows us to elucidate the number of quarks induced by a static quark antiquark source, as well as the internal energy of such a pair in dense quark matter. We furthermore determine the screening length, which in the confinement phase is synonymous with the string breaking distance. The screening length is a decreasing function of baryon density, due to the possibility to break the interquark string via a scalar diquark condensate at high density. We also study the large distance properties of the color singlet grand potential in a dense medium and find that it is well described by a simple Debye screening formula, parameterized by a Debye mass and an effective coupling constant. The latter is of order of unity, i.e. even at large density two-color quark matter is a strongly correlated system.

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arXiv2018

Lattice QCD thermodynamics at finite chemical potential and its comparison with Experiments

We compare higher moments of baryon numbers measured at the RHIC heavy ion collision experiments with those by the lattice QCD calculations. We employ the canonical approach, in which we can access the real chemical potential regions avoiding the sign problem. In the lattice QCD simulations, we study several fits of the number density in the pure imaginary chemical potential, and analyze how these fits affects behaviors at the real chemical potential. In the energy regions between $\sqrt{s}_{NN}$=19.6 and 200 GeV, the susceptibility calculated at $T/T_c=0.93$ is consistent with experimental data at $0 \le μ_B/T < 1.5$, while the kurtosis shows similar behavior with that of the experimental data in the small $μ_B/T$ regions $0 \le μ_B/T < 0.3$. The experimental data at $\sqrt{s}_{NN}=$ 11.5 shows quite different behavior. The lattice result in the deconfinement region,$T/T_c=1.35$, is far from experimental data.

hep-lat↗
arXiv2018

Lee-Yang zeros in lattice QCD for searching phase transition points

We report Lee-Yang zeros behavior at finite temperature and density. The quark number densities, , are calculated at the pure imaginary chemical potential, where no sign problem occurs. Then, the canonical partition functions, Z_C(n,T,V), up to some maximal values of n are estimated through fitting theoretically motivated functions to , which are used to compute the Lee-Yang zeros. We study the temperature dependence of the distributions of the Lee-Yang zeros around the pseudo-critical temperature region T/T_c = 0.84 - 1.35. In the distributions of the Lee-Yang zeros, we observe the Roberge-Weiss phase transition at T/T_c >= 1.20. We discuss the dependence of the behaviors of Lee-Yang zeros on the maximal value of n, so that we can estimate a reliable infinite volume limit.

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arXiv2018

The $\big\langle A^2 \big\rangle$ Asymmetry and Longitudinal Propagator in Lattice $SU(2)$ Gluodynamics at $T\simeq T_c$

We study numerically the chromoelectric-chromomagnetic asymmetry of the dimension two gluon condensate as well as the longitudinal gluon propagator at $T\simeq T_c$ in the Landau-gauge $SU(2)$ lattice gauge theory. We show that substantial correlation between the asymmetry and the Polyakov loop as well as the correlation between the longitudinal propagator and the Polyakov loop pave the way to studies of the critical behavior of the asymmetry and the longitudinal propagator. The respective values of critical exponents and amplitudes are evaluated.

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