Perturbation theory for the logarithm of a positive operator
Name
13130_2023_Article_22172.pdf
Size
385.93 KB
Format
Adobe PDF
Checksum (MD5)
027d6136aa9fbe90f2bcc9be1fb72aa3
Author(s)
Lashkari, Nima
Liu, Hong
Rajagopal, Srivatsan
Date Issued
November 16, 2023
Publisher
Springer Berlin Heidelberg
Citation
Journal of High Energy Physics. 2023 Nov 16;2023(11):97
Version
Final published version
Abstract
Abstract
In various contexts in mathematical physics, such as out-of-equilibrium physics and the asymptotic information theory of many-body quantum systems, one needs to compute the logarithm of a positive unbounded operator. Examples include the von Neumann entropy of a density matrix and the flow of operators with the modular Hamiltonian in the Tomita-Takesaki theory. Often, one encounters the situation where the operator under consideration, which we denote by ∆, can be related by a perturbative series to another operator ∆0, whose logarithm is known. We set up a perturbation theory for the logarithm log ∆. It turns out that the terms in the series possess a remarkable algebraic structure, which enables us to write them in the form of nested commutators plus some “contact terms”.
MIT Department
Massachusetts Institute of Technology. Center for Theoretical Physics
Terms of Use
Creative Commons Attribution
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1007/JHEP11(2023)097
