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We develop a flow-based sampling algorithm for $SU(N)$ lattice gauge theories that is gauge-invariant by construction. Our key contribution is constructing a class of flows on an $SU(N)$ variable (or on a $U(N)$ variable by a simple alternative) that respect matrix conjugation symmetry. We apply this technique to sample distributions of single $SU(N)$ variables and to construct flow-based samplers for $SU(2)$ and $SU(3)$ lattice gauge theory in two dimensions., Comment: 24 pages, 19 figures

International audience; 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, we show that the algorithm may be trained to build up the Polyakov loop which serves an order parameter of the deconfining phase transition. The machine learning techniques can thus 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.

We define a class of machine-learned flow-based sampling algorithms for lattice gauge theories that are gauge-invariant by construction. We demonstrate the application of this framework to U(1) gauge theory in two spacetime dimensions, and find that near critical points in parameter space the approach is orders of magnitude more efficient at sampling topological quantities than more traditional sampling procedures such as Hybrid Monte Carlo and Heat Bath., 6 pages, 4 figures

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., Comment: 8 pages, 8 figures and 2 tables

We discuss our study for exploring the QCD phase diagram based on the lattice QCD. To go beyond the Taylor expansion and to reach higher density regions, we employ the canonical approach. In order to produce lattice data which meet experimental situation as much as possible, we propose a canonical approach with the charge and baryon number. We present our lattice QCD GPU code for this project which employs the clover improved Wilson fermions and Iwasaki gauge action to investigate pure imaginary chemical potential.

A novel approach to the problem of deriving the generating functional for the canonical ensemble in lattice QCD at a nonzero chemical potential is proposed. The derivation proceeds in several steps. First, the baryon density for imaginary values of the chemical potential is obtained. Then, again for imaginary values of the chemical potential, the generating functional of the grand canonical ensemble is derived. In this analysis, a fit of baryon density is employed toward simplifying the procedure of numerical integration. Finally, the generating potential for the canonical ensemble is derived using a high-precision numerical Fourier transform. The generating functional for the canonical ensemble is also derived using the known hopping-parameter expansion, and the results obtained with the two methods are compared for the deconfinement phase in the lattice QCD with two flavors.

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 $\sigma_{\parallel}$ and perpendicular $\sigma_{\perp}$ 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 $\sigma_{\parallel}$ grows whereas $\sigma_{\perp}$ 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 $\sigma_{\parallel, \perp}$ 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., Comment: 6 pages, 4 figures

The canonical approach is a powerful tool to circumvent sign problem in LQCD. Although it has its own difficulties it provides opportunity to determine QCD phase transition line. Using improved Wilson fermions we calculated number density at nonzero imaginary chemical potential for confinement and deconfinement phases, restored canonical partition functions Zn and did extrapolation into the real chemical potential region. We computed the higher moments of the baryon number including the kurtosis, and compared our results with information from relativistic heavy ion collision experiments.

A computer model to simulate the processes of charge injection and migration through DNA after irradiation by a heavy charged particle was developed. The most probable sites of charge injection were obtained by merging spatial models of short DNA sequence and a single 1 GeV/u iron particle track simulated by the code RITRACKS (Relativistic Ion Tracks). Charge migration was simulated by using a quantum-classical nonlinear model of the DNA-charge system. It was found that charge migration depends on the environmental conditions. The oxidative damage in DNA occurring during hole migration was simulated concurrently, which allowed the determination of probable locations of radiation-induced DNA lesions.

This paper provides results of numerical simulations of graphene conductivity. The numerical results were performed in tight-biding model with Coulomb potential screened by σ electron of carbon atoms. The dependence of the graphene conductivity on the dielectric permittivity of substrate was calculated. The results agreeds with experimental data.

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., This work has been supported by Spain’s MINECO under Grant No. FIS2014-57432-P, by the Comunidad de Madrid under Grant No. S2013/MIT-3007 MAD2D-CM, and by Germany’s Deutsche Forschungsgemeinschaft (DFG) via SFB 689. The work of M. V. U. was supported by DFG Grant No. BU 2626/2-1. D. L. B. acknowledges the support by RFBR Grant No. 16-32-00362-mol-a., S2013/MIT-3007/MAD2D-CM

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 $i{\ensuremath{\mu}}_{qI}$. Then we restore the grand canonical partition function for imaginary chemical potential using the 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 the 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.

The canonical approach, which was developed for solving the sign problem, may suffer from a new type of sign problem. In the canonical approach, the grand partition function is written as a fugacity expansion: $Z_G(\mu,T) = \sum_n Z_C(n,T) \xi^n$, where $\xi=\exp(\mu/T)$ is the fugacity, and $Z_C(n,T)$ are given as averages over a Monte Carlo update, $\langle z_n\rangle$. We show that the complex phase of $z_n$ is proportional to $n$ at each Monte Carlo step. Although $\langle z_n\rangle$ take real positive values, the values of $z_n$ fluctuate rapidly when $n$ is large, especially in the confinement phase, which gives a limit on $n$. We discuss possible remedies for this problem., Comment: 7 pages, 6 figures

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., Comment: 10 pages, 5 figures, Contribution to XIIth Quark Confinement and the Hadron Spectrum

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., Comment: 6 pages, 7 figures, contribution to XXIII International Baldin Seminar on High Energy Physics Problems "Relativistic Nuclear Physics and Quantum Chromodynamics", 19-24 September, 2016, Dubna, Russia. arXiv admin note: text overlap with arXiv:1611.08344

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., 8 pages, 4 figures, Contribution to XIIth Quark Confinement and the Hadron Spectrum

Optical conductivity of graphene is studied using Quantum Monte Carlo calculations. We start from Euclidean current-current correlator and extract $\sigma (\omega)$ 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 $\omega \approx \kappa$ thus working in the region of the plateau in $\sigma(\omega)$ 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., Comment: text is expanded, figures are updated, accepted for publication in Phys. Rev. B

Using GPGPU techniques and multi-precision calculation we developed the code to study QCD phase transition line in the canonical approach. The canonical approach is a powerful tool to investigate sign problem in Lattice QCD. The central part of the canonical approach is the fugacity expansion of the grand canonical partition functions. Canonical partition functions $Z_n(T)$ are coefficients of this expansion. Using various methods we study properties of $Z_n(T)$. At the last step we perform cubic spline for temperature dependence of $Z_n(T)$ at fixed $n$ and compute baryon number susceptibility $\chi_B/T^2$ as function of temperature. After that we compute numerically $\partial\chi/ \partial T$ and restore crossover line in QCD phase diagram. We use improved Wilson fermions and Iwasaki gauge action on the $16^3 \times 4$ lattice with $m_{\pi}/m_{\rho} = 0.8$ as a sandbox to check the canonical approach. In this framework we obtain coefficient in parametrization of crossover line $T_c(\mu_B^2)=T_c\left(c-\kappa\, \mu_B^2/T_c^2\right)$ with $\kappa = -0.0453 \pm 0.0099$., Comment: 6 pages, 5 figures

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., 8 pages, 8 figures, Contribution to ICNFP2017, to be published in EPJ Web of Conferences

A hole transport through DNA base sequences was modeled. The fact that DNA consists of two polynucleotide strands was taken into consideration. Specific DNA base locations are determined in the model. The model predicts the behavior of a hole acting on the DNA chain, taking into account reversible and irreversible dynamics. It was shown that the transfer mechanisms depend on the sequence type and can be either of hopping nature or of superexchange one. Distance dependence of the hole transport relative rate on the number of hopping steps was investigated. The results obtained were compared with the experimental data. The investigation demonstrates the utilization of the formalism in practical problems for description of the charge migration through the different molecular sequences.

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., Comment: 6 pages, 5 figures. arXiv admin note: substantial text overlap with arXiv:1204.0921