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MPSTimeEvolution.jl

This is the documentation for the MPSTimeEvolution.jl package.

This package implements time-evolution algorithms for tensor networks. It is based on the ITensor library.

Package features

The package implements:

  • the one-site time-dependent variational principle (TDVP1) [1–3], in its standard version as well as
    • its variant with adaptive bond dimensions [4],
    • a non-unitary version (for vectorised mixed states);
  • matrix-product states in the Vidal (or canonical) gauge,
  • the time-evolving block-decimation algorithm (TEBD) for Vidal-form MPS, together with automatic 1st and 2nd order Suzuki-Trotter decompositions.

See Reference for a complete list of features, and a description of the available methods. The Tutorial section contains step-by-step examples on how to use the key features of this package.

Bibliography

[1]
C. Lubich, I. Oseledets and B. Vandereycken. Time Integration of Tensor Trains. SIAM Journal on Numerical Analysis 53, 917–941 (2015).
[2]
J. Haegeman, C. Lubich, I. Oseledets, B. Vandereycken and F. Verstraete. Unifying time evolution and optimization with matrix product states. Physical Review B 94 (2016).
[3]
S. Paeckel, T. Köhler, A. Swoboda, S. R. Manmana, U. Schollwöck and C. Hubig. Time-evolution methods for matrix-product states. Annals of Physics 411 (2019).
[4]
A. J. Dunnett and A. W. Chin. Efficient bond-adaptive approach for finite-temperature open quantum dynamics using the one-site time-dependent variational principle for matrix product states. Physical Review B 104 (2021).
[5]
M. Schmutz. Real-Time Green's Functions in Many Body Problems. Zeitschrift für Physik B Condensed Matter 30, 97–106 (1978).
[6]
M. Brenes, J. J. Mendoza-Arenas, A. Purkayastha, M. T. Mitchison, S. R. Clark and J. Goold. Tensor-Network Method to Simulate Strongly Interacting Quantum Thermal Machines. Physical Review X 10 (2020).
[7]
G. Vidal. Efficient Classical Simulation of Slightly Entangled Quantum Computations. Physical Review Letters 91 (2003).
[8]
U. Schollwöck. The density-matrix renormalization group in the age of matrix product states. Annals of Physics 326, 96–192 (2011).
[9]