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We present an expression for the spectral gap, opening up new possibilities for performing and accelerating spectral calculations of quantum many-body systems. We develop and demonstrate one such possibility in the context of tensor network simulations. Our approach requires only minor modifications of the widely used simple update method and is computationally lightweight relative to other approaches. We validate it by computing spectral gaps of the 2D and 3D transverse-field Ising models and find strong agreement with previously reported perturbation theory results., Comment: 1D Haldane chain model analyzed (7 pages and 5 figures)

We develop a new methodology to contract tensor networks within the corner transfer matrix renormalization group approach for a wide range of two-dimensional lattice geometries. We discuss contraction algorithms on the example of triangular, kagome, honeycomb, square-octagon, star, ruby, square-hexagon-dodecahedron, and dice lattices. As benchmark tests, we apply the developed method to the classical Ising model on different lattices and observe a remarkable agreement of the results with the available from the literature. The approach also shows the necessary potential to be applied to various quantum lattice models in a combination with the wave-function variational optimization schemes., Comment: 29 pages, 47 figures, final version

We develop a method of variational optimization of the infinite projected entangled pair states on the honeycomb lattice. The method is based on the automatic differentiation of the honeycomb-lattice corner transfer matrix renormalization group. We apply the approach to the antiferromagnetic Heisenberg spin-1/2 and ferromagnetic Kitaev models on the honeycomb lattice. The developed formalism gives quantitatively accurate results for the main physical observables and has a necessary potential for further extensions., Comment: 7 pages, 7 figures, published version

We develop the continuous matrix-product states approach for description of inhomogeneous one-dimensional quantum systems with long-range interactions. The method is applied to the exactly-solvable Calogero-Moser model. We show the high accuracy of reproducing the ground-state properties of the many-body system and discuss potential errors that can originate from the approximation of the nonlocal interaction potentials with singularities.

We study theoretically transitions between the localized and chaotic many-body regimes in one-dimensional quantum lattice systems with long-range couplings between particles and linear external potential. In terms of established criteria characterizing localization, we construct effective phase diagrams for several types of lattice systems with variable amplitude of the external linear tilt and interaction strength. By means of exact diagonalization and time-dependent variational principle numerical approaches we analyze system dynamics after quenches. Our results reveal that the Stark localization without any artificial source of disorder remains stable upon inclusion of long-range interactions., Comment: published version, 14 pages, 11 figures

We study theoretically a gas consisting of charged bosons (ions) over the flat dielectric surface at low temperatures and its tendency to form a state with a Bose-Einstein condensate. For the stability of a system, an additional external electric field, which keeps charges at the dielectric surface, is introduced. The formalism is developed in the framework of a self-consistent-field approach, which combines the quasiclassical description in terms of the Wigner distribution functions and the quantum-mechanical approach by employing the Gross-Pitaevskii equation. We predict a formation of the state with a Bose-Einstein condensate and determine the near-critical physical characteristics of the system. It is shown that the thermal and condensate components become spatially separated under these conditions. We discuss the limitations of the developed semiclassical approach and prospects for the pure quantum-mechanical treatment of the problem., Comment: 9 pages, 6 figures

We present the results of 3D-hydrodynamical simulations of accretion flow in the eclipsing dwarf nova V1239 Her in quiescence. The model includes the optical star filling its Roche lobe, a gas stream emanating from the inner Lagrangian point of the binary system, and the accretion disc structure. A cold hydrogen gas stream is initially emitted towards a point-like gravitational centre. A stationary accretion disc is formed in about 15 orbital periods after the beginning of accretion. The model takes into account partial ionization of hydrogen and uses realistic cooling function for hydrogen. The light curve of the system is calculated as the volume emission of optically thin layers along the line of sight up to the optical depth \tau =2/3 calculated using Planck-averaged opacities. The calculated eclipse light curves show good agreement with observations, with the changing shape of pre-eclipse and post-eclipse light curves being explained entirely due to ~ 50% variations in the mass accretion rate through the gas stream., Comment: 8 pages, 8 figures, 1 movie (ancillary file). Accepted for publication in MNRAS