Time-evolution methods for matrix-product states

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 WI,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…

• DF
  Deutsche Forschungsgemeinschaft

  Awards: EXC-2111, EXC-2111 \u2013 390814868, ERC-2017-STG, SFB/CRC1073, 207383564, 217133147, FOR 1807, CRC1073, B03)- 217133147, P7) \u2013 207383564, 390814868
• ER
  European Research Council

  Awards: 742102, 758935