SciPost Physics Core

SciPost Phys. Core 4, 004 (2021) · published 19 February 2021

• doi: 10.21468/SciPostPhysCore.4.1.004
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Abstract

A central primitive in quantum tensor network simulations is the problem of approximating a matrix product state with one of a lower bond dimension. This problem forms the central bottleneck in algorithms for time evolution and for contracting projected entangled pair states. We formulate a tangent-space based variational algorithm to achieve this for uniform (infinite) matrix product states. The algorithm exhibits a favourable scaling of the computational cost, and we demonstrate its usefulness by several examples involving the multiplication of a matrix product state with a matrix product operator.

• Van Damme et al., Efficient higher-order matrix product operators for time evolution
  SciPost Phys. 17, 135 (2024) [Crossref]
• Dunnett et al., Efficient bond-adaptive approach for finite-temperature open quantum dynamics using the one-site time-dependent variational principle for matrix product states
  Phys. Rev. B 104, 214302 (2021) [Crossref]
• Link et al., Open Quantum System Dynamics from Infinite Tensor Network Contraction
  Phys. Rev. Lett. 132, 200403 (2024) [Crossref]
• Li et al., Time-Dependent Variational Principle with Controlled Bond Expansion for Matrix Product States
  Phys. Rev. Lett. 133, 026401 (2024) [Crossref]
• Fishman et al., The ITensor Software Library for Tensor Network Calculations
  SciPost Phys. Codebases, 4 (2022) [Crossref]
• Zhang et al., Differentiable programming tensor networks for Kitaev magnets
  Phys. Rev. B 108, 085103 (2023) [Crossref]
• Montangero et al., Loop-free tensor networks for high-energy physics
  Phil. Trans. R. Soc. A. 380, 20210065 (2022) [Crossref]
• Wu et al., Two-dimensional isometric tensor networks on an infinite strip
  Phys. Rev. B 107, 245118 (2023) [Crossref]
• Vanderstraeten et al., Variational methods for contracting projected entangled-pair states
  Phys. Rev. B 105, 195140 (2022) [Crossref]
• Yang et al., Projected d -wave superconducting state: A fermionic projected entangled pair state study
  Phys. Rev. B 107, 125128 (2023) [Crossref]
• Colbois et al., Partial lifting of degeneracy in the J1−J2−J3 Ising antiferromagnet on the kagome lattice
  Phys. Rev. B 106, 174403 (2022) [Crossref]