Time-evolution methods for matrix-product states

作者：Sebastian Paeckel, Thomas Köhler, Andreas Swoboda, Salvatore R. Manmana, Ulrich Schollwöck, Claudius Hubig · 发表于：Annals of Physics · 年份：2019 · DOI：10.1016/j.aop.2019.167998 · 被引用次数：669 · 研究领域：Quantum many-body systems、Quantum Mechanics and Non-Hermitian Physics、Cold Atom Physics and Bose-Einstein Condensates

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 of current problem settings in condensed matter physics.