Secularly growing loop corrections in strong electric fields

We calculate one--loop corrections to the vertexes and propagators of photons and charged particles in the strong electric field backgrounds. We use the Schwinger--Keldysh diagrammatic technique. We observe that photon's Keldysh propagator receives growing with time infrared contribution. As the result, loop corrections are not suppressed in comparison with tree--level contribution. This effect substantially changes the standard picture of the pair production. To sum up leading IR corrections from all loops we consider the infrared limit of the Dyson--Schwinger equations and reduce them to a single kinetic equation.Comment: 16 pages, no figures; Minor correction

Many-body effects in graphene beyond the Dirac model with Coulomb interaction

This paper is devoted to development of perturbation theory for studying the properties of graphene sheet of finite size, at nonzero temperature and chemical potential. The perturbation theory is based on the tight-binding Hamiltonian and arbitrary interaction potential between electrons, which is considered as a perturbation. One-loop corrections to the electron propagator and to the interaction potential at nonzero temperature and chemical potential are calculated. One-loop formulas for the energy spectrum of electrons in graphene, for the renormalized Fermi velocity and also for the dielectric permittivity are derived.Comment: 11 pages, 11 figure

Study of shear viscosity of SU (2)-gluodynamics within lattice simulation

This paper is devoted to the study of two-point correlation function of the energy-momentum tensor T_{12}T_{12} for SU(2)-gluodynamics within lattice simulation of QCD. Using multilevel algorithm we carried out the measurement of the correlation function at the temperature T/T_c = 1.2. It is shown that lattice data can be described by spectral functions which interpolate between hydrodynamics at low frequencies and asymptotic freedom at high frequencies. The results of the study of spectral functions allowed us to estimate the ratio of shear viscosity to the entropy density {\eta}/s = 0.134 +- 0.057.Comment: 7 pages, 3 figure

Quantum Monte Carlo study of static potential in graphene

In this paper the interaction potential between static charges in suspended graphene is studied within the quantum Monte Carlo approach. We calculated the dielectric permittivity of suspended graphene for the set of temperatures and extrapolated our results to zero temperature. The dielectric permittivity at zero temperature has the following properties. At zero distance $\epsilon=2.24\pm0.02$. Then it rises and at a large distance the dielectric permittivity reaches the plateau $\epsilon\simeq4.20\pm0.66$. The results obtained in this paper allow to draw a conclusion that full account of many-body effects in the dielectric permittivity of suspended graphene gives $\epsilon$ very close to the one-loop results. Contrary to the one-loop result, the two-loop prediction for the dielectric permittivity deviates from our result. So, one can expect large higher order corrections to the two-loop prediction for the dielectric permittivity of suspended graphene.Comment: 6 pages, 2 figure

Generalization properties of neural network approximations to frustrated magnet ground states

Neural quantum states (NQS) attract a lot of attention due to their potential to serve as a very expressive variational ansatz for quantum many-body systems. Here we study the main factors governing the applicability of NQS to frustrated magnets by training neural networks to approximate ground states of several moderately-sized Hamiltonians using the corresponding wave function structure on a small subset of the Hilbert space basis as training dataset. We notice that generalization quality, i.e. the ability to learn from a limited number of samples and correctly approximate the target state on the rest of the space, drops abruptly when frustration is increased. We also show that learning the sign structure is considerably more difficult than learning amplitudes. Finally, we conclude that the main issue to be addressed at this stage, in order to use the method of NQS for simulating realistic models, is that of generalization rather than expressibility

Generalization properties of neural network approximations to frustrated magnet ground states

Neural quantum states (NQS) attract a lot of attention due to their potential to serve as a very expressive variational ansatz for quantum many-body systems. Here we study the main factors governing the applicability of NQS to frustrated magnets by training neural networks to approximate ground states of several moderately-sized Hamiltonians using the corresponding wave function structure on a small subset of the Hilbert space basis as training dataset. We notice that generalization quality, i.e. the ability to learn from a limited number of samples and correctly approximate the target state on the rest of the space, drops abruptly when frustration is increased. We also show that learning the sign structure is considerably more difficult than learning amplitudes. Finally, we conclude that the main issue to be addressed at this stage, in order to use the method of NQS for simulating realistic models, is that of generalization rather than expressibility. © 2020, The Author(s).Russian Science Foundation, RSF: 18-12-00185, 16-12-10059Alexander von Humboldt-Stiftung: 0033-2019-0002Nederlandse Organisatie voor Wetenschappelijk Onderzoek, NWOEuropean Research Council, ERC: 338957 FEMTO/ NANOWe are thankful to Dmitry Ageev and Vladimir Mazurenko for collaboration during the early stages of the project. We have significantly benefited from encouraging discussions with Giuseppe Carleo, Juan Carrasquilla, Askar Iliasov, Titus Neupert, and Slava Rychkov. The research was supported by the ERC Advanced Grant 338957 FEMTO/ NANO and by the NWO via the Spinoza Prize. The work of A.A.B. which consisted of designing the project (together with K.S.T.), implementation of prototype version of the code, and providing general guidance, was supported by Russian Science Foundation, Grant no. 18-12-00185. The work of N.A. which consisted of numerical experiments, was supported by the Russian Science Foundation Grant no. 16-12-10059. N.A. acknowledges the use of computing resources of the federal collective usage center Complex for Simulation and Data Processing for Mega-science Facilities at NRC "Kurchatov Institute”, http://ckp.nrcki.ru/. K.S.T. is supported by Alexander von Humboldt Foundation and by the program 0033-2019-0002 by the Ministry of Science and Higher Education of Russia

NetKet 3: Machine Learning Toolbox for Many-Body Quantum Systems

We introduce version 3 of NetKet, the machine learning toolbox for many-body quantum physics. NetKet is built around neural-network quantum states and provides efficient algorithms for their evaluation and optimization. This new version is built on top of JAX, a differentiable programming and accelerated linear algebra framework for the Python programming language. The most significant new feature is the possibility to define arbitrary neural network ansätze in pure Python code using the concise notation of machine-learning frameworks, which allows for just-in-time compilation as well as the implicit generation of gradients thanks to automatic differentiation. NetKet 3 also comes with support for GPU and TPU accelerators, advanced support for discrete symmetry groups, chunking to scale up to thousands of degrees of freedom, drivers for quantum dynamics applications, and improved modularity, allowing users to use only parts of the toolbox as a foundation for their own code