arXiv subjects
Publications and source records attributed to I. V. Lukin.
We study the ground state of the SU(4) Heisenberg model on the hyperhoneycomb lattice using three-dimensional projected entangled pair states. We show that it is possible to compute physical observables for the ground states using loop expansions, which converge quickly on tree-like lattices. Our extrapolations to the limit of infinite bond dimensions point toward gapless spin-liquid ground state.
We study ground-state properties and phase diagram of the $J_{1}$-$J_{2}$ antiferromagnetic XY model on the honeycomb lattice by means of the developed corner transfer matrix renormalization group algorithm with the two-site unit cell and the infinite spiral projected entangled pair states ansatz. We identify the main phases: Néel, Ising, collinear, and incommensurate spiral phases, as well as the transitions between them, as functions of the ratio $J_{2}/J_{1}$. In the regime of competing types of ordering, we show that the energies of the dimerized states are systematically higher than the energies in the collinear phase. This collinear phase transforms to the incommensurate spiral phase through the second-order phase transition upon a further increase of $J_2/J_1$.
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.
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.
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.
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.