2019/01/31 by Sebastian Paeckel, Thomas Köhler, Andreas Swoboda +3 · 2 citations
Physics and Astronomy · #cond-mat.str-el #cond-mat.stat-mech #quant-ph
paper · pdf · doi:10.1016/j.aop.2019.167998
published as Annals of Physics 411, 167998 (2019) · Content identical to final journal version, plus a table of contents and minus some formatting errors
arxiv created 2019/11/14 · arxiv updated 2019/11/15
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 WII 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.