arXiv subjects

D. L. Boyda

Publications and source records attributed to D. L. Boyda.

12 recordsLinked to original sources

arXiv2022

Applying machine learning methods to prediction problems of lattice observables

We discuss the prediction of critical behavior of lattice observables in SU(2) and SU(3) gauge theories. We show that feed-forward neural network, trained on the lattice configurations of gauge fields as input data, finds correlations with the target observable, which is also true in the critical region where the neural network has not been trained. We have verified that the neural network constructs a gauge-invariant function and this property does not change over the entire range of the parameter space.

hep-lat↗

arXiv2020

Machine-learning physics from unphysics: Finding deconfinement temperature in lattice Yang-Mills theories from outside the scaling window

We study the machine learning techniques applied to the lattice gauge theory's critical behavior, particularly to the confinement/deconfinement phase transition in the SU(2) and SU(3) gauge theories. We find that the neural network, trained on lattice configurations of gauge fields at an unphysical value of the lattice parameters as an input, builds up a gauge-invariant function, and finds correlations with the target observable that is valid in the physical region of the parameter space. In particular, if the algorithm aimed to predict the Polyakov loop as the deconfining order parameter, it builds a trace of the gauge group matrices along a closed loop in the time direction. As a result, the neural network, trained at one unphysical value of the lattice coupling $β$ predicts the order parameter in the whole region of the $β$ values with good precision. We thus demonstrate that the machine learning techniques may be used as a numerical analog of the analytical continuation from easily accessible but physically uninteresting regions of the coupling space to the interesting but potentially not accessible regions.

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.

hep-lat↗

arXiv2017

Lattice Quantum Monte Carlo Study of Chiral Magnetic Effect in Dirac Semimetals

In this paper Chiral Magnetic Effect (CME) in Dirac semimetals is studied by means of lattice Monte Carlo simulation. We measure conductivity of Dirac semimetals as a function of external magnetic field in parallel $σ_{\parallel}$ and perpendicular $σ_{\perp}$ to the external field directions. The simulations are carried out in three regimes: semimetal phase, onset of the insulator phase and deep in the insulator phase. In the semimetal phase $σ_{\parallel}$ grows whereas $σ_{\perp}$ drops with magnetic field. Similar behaviour was observed in the onset of the insulator phase but conductivity is smaller and its dependence on magnetic field is weaker. Finally in the insulator phase conductivities $σ_{\parallel, \perp}$ are close to zero and do not depend on magnetic field. In other words, we observe manifestation of the CME current in the semimetal phase, weaker manifestation of the CME in the onset of the insulator phase. We do not observe signatures of CME in the insulator phase. We believe that the suppression of the CME current in the insulator phase is connected to chiral symmetry breaking and generation of dynamical fermion mass which take place in this phase.

cond-mat.str-el↗

arXiv2017

Lattice QCD at finite baryon density using analytic continuation

We simulate lattice QCD with two flavors of Wilson fermions at imaginary baryon chemical potential. Results for the baryon number density computed in the confining and deconfining phases at imaginary baryon chemical potential are used to determine the baryon number density and higher cumulants at the real chemical potential via analytical continuation.

hep-lat↗

arXiv2017

Interacting Electrons in Graphene: Fermi Velocity Renormalization and Optical Response

We have developed a Hartree-Fock theory for electrons on a honeycomb lattice aiming to solve a long-standing problem of the Fermi velocity renormalization in graphene. Our model employs no fitting parameters (like an unknown band cutoff) but relies on a topological invariant (crystal structure function) that makes the Hartree-Fock sublattice spinor independent of the electron-electron interaction. Agreement with the experimental data is obtained assuming static self-screening including local field effects. As an application of the model, we derive an explicit expression for the optical conductivity and discuss the renormalization of the Drude weight. The optical conductivity is also obtained via precise quantum Monte Carlo calculations which compares well to our mean-field approach.

cond-mat.mes-hall↗

arXiv2016

Study of lattice QCD at finite chemical potential using canonical ensemble approach

New approach to computation of canonical partition functions in $N_f=2$ lattice QCD is presented. We compare results obtained by new method with results obtained by known method of hopping parameter expansion. We observe agreement between two methods indicating validity of the new method. We use results for the number density obtained in the confining and deconfining phases at imaginary chemical potential to determine the phase transition line at real chemical potential.

hep-lat↗

arXiv2016

Study of lattice QCD at finite baryon density using the canonical approach

At finite baryon density lattice QCD first-principle calculations can not be performed due to the sign problem. In order to circumvent this problem, we use the canonical approach, which provides reliable analytical continuation from the imaginary chemical potential region to the real chemical potential region. We briefly present the canonical partition function method, describe our formulation, and show the results, obtained for two temperatures: $T/T_c = 0.93$ and $T/T_c = 0.99$ in lattice QCD with two flavors of improved Wilson fermions.

hep-lat↗

arXiv2016

Dyons and Roberge - Weiss transition in lattice QCD

We study lattice QCD with $N_f=2$ Wilson fermions at nonzero imaginary chemical potential and nonzero temperature. We relate the Roberge - Weiss phase transition to the properties of dyons which are constituents of the KvBLL calorons. We present numerical evidence that the characteristic features of the spectral gap of the overlap Dirac operator as function of an angle modifying the boundary condition are determined by the $Z_3$ sector of the respective imaginary chemical potential. We then demonstrate that dyon excitations in thermal configurations could be responsible (in line with perturbative excitations) for these phenomena.

hep-lat↗

arXiv2016

New approach to canonical partition functions computation in $N_f=2$ lattice QCD at finite baryon density

We propose and test a new approach to computation of canonical partition functions in lattice QCD at finite density. We suggest a few steps procedure. We first compute numerically the quark number density for imaginary chemical potential $iμ_{qI}$. Then we restore the grand canonical partition function for imaginary chemical potential using fitting procedure for the quark number density. Finally we compute the canonical partition functions using high precision numerical Fourier transformation. Additionally we compute the canonical partition functions using known method of the hopping parameter expansion and compare results obtained by two methods in the deconfining as well as in the confining phases. The agreement between two methods indicates the validity of the new method. Our numerical results are obtained in two flavor lattice QCD with clover improved Wilson fermions.

hep-lat↗

arXiv2016

Many-body effects on graphene conductivity: Quantum Monte Carlo calculations

Optical conductivity of graphene is studied using Quantum Monte Carlo calculations. We start from Euclidean current-current correlator and extract $σ(ω)$ from Green-Kubo relations using Backus-Gilbert method. Calculations were performed both for long-range interactions and taking into account only contact term. In both cases we vary interaction strength and study its influence on optical conductivity. We compare our results with previous theoretical calculations choosing $ω\approx κ$ thus working in the region of the plateau in $σ(ω)$ which corresponds to optical conductivity of Dirac quasiparticles. No dependence of optical conductivity on interaction strength is observed unless we approach antiferromagnetic phase transition in case of artificially enhanced contact term. Our results strongly support previous theoretical studies claimed very weak regularization of graphene conductivity.

cond-mat.str-el↗

arXiv2013

Numerical simulation of graphene in external magnetic field

In this paper the results of numerical simulation of monolayer graphene in external magnetic field are presented. The numerical simulation is performed in the effective lattice field theory with noncompact $3 + 1$-dimensional Abelian lattice gauge fields and $2 + 1$-dimensional staggered lattice fermions. The dependences of fermion condensate and graphene conductivity on the dielectric permittivity of substrate for different values of external magnetic field are calculated. It is found that magnetic field shifts insulator-semimetal phase transition to larger values of the dielectric permittivity of substrate. The phase diagram of graphene in external magnetic field is drawn.

hep-lat↗