Calculating Elements of Matrix Functions using Divided Differences

Lev Barash, Stefan Güttel, Itay Hen

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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 264 × 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.
Original languageEnglish
JournalComputer Physics Communications
Early online date11 Nov 2021
DOIs
Publication statusPublished - 1 Feb 2022

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