Filter (signal processing)

Matrix (chemical analysis)

Algorithm

Physics

Statistical physics

Composite material

Matrix multiplication

Decimation

Political science

Materials science

Geometry

Representation (politics)

Matrix product state

Applied mathematics

Computer vision

Theoretical physics

Mathematics

Computer science

State (computer science)

Quantum mechanics

Quantum

Product (mathematics)

Politics

Annals of Physics

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.

Time-evolution methods for matrix-product states