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- W3174134809 abstract "Tensor network states are expected to be good representations of a large class of interesting quantum many-body wave functions. In higher dimensions, their utility is however severely limited by the difficulty of contracting the tensor network, an operation needed to calculate quantum expectation values. Here we introduce a method for the time evolution of three-dimensional isometric tensor networks which respects the isometric structure and therefore renders contraction simple through a special canonical form. Our method involves a tetrahedral site splitting which allows one to move the orthogonality center of an embedded tree tensor network in a simple cubic lattice to any position. Using imaginary time evolution to find an isometric tensor network representation of the ground state of the three-dimensional transverse field Ising model across the entire phase diagram, we perform a systematic benchmark study of this method in comparison with exact Lanczos and quantum Monte Carlo results. We show that the obtained energy matches the exact ground-state result accurately deep in the ferromagnetic and polarized phases, while the regime close to the critical point requires larger bond dimensions. This behavior is in close analogy with the two-dimensional case, which we also discuss for comparison.10 MoreReceived 2 June 2020Revised 3 June 2021Accepted 3 June 2021DOI:https://doi.org/10.1103/PhysRevResearch.3.023236Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Open access publication funded by the Max Planck Society.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasMagnetismQuantum phase transitionsPhysical Systems3-dimensional systemsTechniquesSpin lattice modelsTensor network methodsVariational approachCondensed Matter & Materials Physics" @default.
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- W3174134809 date "2021-06-22" @default.
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- W3174134809 title "Three-dimensional isometric tensor networks" @default.
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