5 citations · 5 across the 4 of their papers we have counts for
5 papers
CTMRG as a tensor-network message-passing algorithm
Illia Lukin, Andrii Sotnikov
We formulate the corner transfer matrix equations, and the corner transfer matrix renormalization group built on them, as a set of local equations on general planar graphs. These e…
Dimerization in the SU(4) Heisenberg model on the cubic lattice: iPEPS study
Illia Lukin, Andrii Sotnikov
We study SU(4)-symmetric Heisenberg model on the cubic lattice with spatially anisotropic magnetic couplings. We utilize several approaches based on the tensor-network representati…
Many-body localization in a quantum Ising model with the long-range interaction: Accurate determination of the transition point
Illia Lukin, Andrii Sotnikov, Alexander L. Burin
Many-body localization (MBL) transition emerges at strong disorder in interacting systems, separating chaotic and reversible dynamics. Although the existence of MBL transition with…
Entanglement scaling in matrix product state representation of smooth functions and their shallow quantum circuit approximations
Vladyslav Bohun, Illia Lukin, Mykola Luhanko +4
Encoding classical data in a quantum state is a key prerequisite of many quantum algorithms. Recently matrix product state (MPS) methods emerged as the most promising approach for…
Single-layer tensor network approach for three-dimensional quantum systems
Illia Lukin, Andrii Sotnikov
Calculation of observables with three-dimensional projected entangled pair states is generally hard, as it requires a contraction of complex multi-layer tensor networks. We utilize…