Time-evolution methods for matrix-product states

By Sebastian Paeckel, T. Kohler, Andreas Swoboda, Salvatore R. Manmana, U. Schollwock, C. Hubig. Annals of Physics, 2019

748 citations recorded by the source corpus.

Matrix-product states have become the de facto standard for the representation of one-dimensional quantum many body states. During the last few years, numerous new methods have been introduced to evaluate the time evolution of a matrix-product state. Here, we will review and summarize the recent work on this topic as applied to finite quantum systems. We will explain and compare the different methods available to construct a time-evolved matrix-product state, namely the time-evolving block decimation, the MPO $W^\mathrm{II}$ method, the global Krylov method, the local Krylov method and the one- and two-site time-dependent variational principle. We will also apply these methods to four different representative examples of current problem settings in condensed matter physics.

Subfields: Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/55e1bd32acf183a8c9d36e54697df8494b3cdd00

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In Atomic and Molecular Physics, and Optics

1. M. Fishman
2. Shenglong Xu
3. S. White
4. E. Stoudenmire
5. Brian Swingle
6. D. Kennes
7. S. Gerber
8. A. D. L. Torre

Citations in the corpus

• What Limits the Simulation of Quantum Computers? (2020, methodology): “[17] Sebastian Paeckel, Thomas Khler, Andreas Swoboda, Salvatore R.”
• Evidence for the utility of quantum computing before fault tolerance (2023, methodology): “Tensor networks have been widely used to approximate and compress quantum state vectors that arise in the study of the low-energy eigenstates of and time evolution by local Hamiltonians 2,32,33 and, more recently, have been successfully used to simulate low-depth noisy quantum circuits 34–36 .”
• The ITensor Software Library for Tensor Network Calculations (2020, background): “Such customizability is important because there are many algorithms available for time-evolving quantum states [54], most of which are not totally black-box and require some care to use well.”
• Scrambling Dynamics and Out-of-Time-Ordered Correlators in Quantum Many-Body Systems (2022, positive): “A large toolbox for manipulating MPS/MPO has been developed over the years [88, 89].”
• Colloquium: Nonthermal pathways to ultrafast control in quantum materials (2021, methodology): “Numerous methods for time evolution have been proposed and benchmarked, including the block decimation, matrix product operator techniques, Krylov methods, or the timedependent variational principle (Paeckel et al., 2019).”