Physics

Pure mathematics

Dimension (graph theory)

Mathematics

Renormalization group

Statistical physics

Matrix (chemical analysis)

Crossover

Matrix multiplication

Artificial intelligence

Composite material

Materials science

Geometry

Matrix product state

Computer science

Quantum mechanics

Product (mathematics)

Density matrix renormalization group

Delocalized electron

Quantum

Physical review. B./Physical review. B

We compare the accuracy of two prime time evolution algorithms involving matrix product states---tDMRG (time-dependent density matrix renormalization group) and TDVP (time-dependent variational principle). The latter is supposed to be superior within a limited and fixed auxiliary space dimension. Surprisingly, we find that the performance of algorithms depends on the model considered. In particular, many-body localized systems as well as the crossover regions between localized and delocalized phases are better described by tDMRG, contrary to the delocalized regime where TDVP indeed outperforms tDMRG in terms of accuracy and reliability. As an example, we study many-body localization transition in a large size Heisenberg chain. We discuss drawbacks of previous estimates [Phys. Rev. B 98, 174202 (2018)] of the critical disorder strength for large systems.

Time dynamics with matrix product states: Many-body localization transition of large systems revisited