Abstract

We introduce a method for calculating individual elements of matrix functions. Our technique makes use of a novel series expansion for the action of matrix functions on basis vectors that is memory efficient even for very large matrices. We showcase our approach by calculating the matrix elements of the exponential of a transverse-field Ising model and evaluating quantum transition amplitudes for large many-body Hamiltonians of sizes up to 2 64× 2 64 on a single workstation. We also discuss the application of the method to matrix inverses. We relate and compare our method to the state-of-the-art and demonstrate its advantages. We also discuss practical applications of our method.

Metadata

publication

Computer Physics Communications 271, 108219, 2022

year

2022

publication date

2022/2/1

authors

Lev Barash, Stefan Güttel, Itay Hen

link

https://www.sciencedirect.com/science/article/pii/S0010465521003313

resource_link

https://arxiv.org/pdf/2107.14124

journal

Computer Physics Communications

volume

271

pages

108219

publisher

North-Holland