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Analytic Time Evolution, Random Phase Approximation, and Green Functions for Matrix Product States

Kinder, Jesse M. and Ralph, Claire C. and Chan, Garnet Kin-Lic (2014) Analytic Time Evolution, Random Phase Approximation, and Green Functions for Matrix Product States. In: Quantum Information and Computation for Chemistry. Advances in Chemical Physics. Vol.154. No.154. John Wiley & Sons, Inc. , Hoboken, NJ, pp. 179-192. ISBN 9781118495667. http://resolver.caltech.edu/CaltechAUTHORS:20170106-121654839

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Abstract

This chapter summarizes the Hartree–Fock (HF) and Matrix product states (MPS) approaches to stationary states to establish notation and illustrate the parallel structure of the theories. It derives analytic equations of motion for MPS time evolution using the Dirac–Frenkel variational principle. The chapter shows that the resulting evolution is optimal for MPS of fixed auxiliary dimension. It discusses the relationship of this approach to time evolution to schemes currently in use. The chapter explains how excitation energies and dynamical properties can be obtained from a linear eigenvalue problem. The relationship of this MPS random phase approximation (RPA) to other dynamical approaches for matrix product states is discussed. Finally, the chapter explores the site-based Green functions that emerge naturally within the theory of MPS and use the fluctuation-dissipation theory to analyze the stationary-state correlations introduced at the level of the MPS RPA.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1002/9781118742631.ch07DOIArticle
http://onlinelibrary.wiley.com/doi/10.1002/9781118742631.ch07/summaryPublisherArticle
https://arxiv.org/abs/1103.2155arXivDiscussion Paper
ORCID:
AuthorORCID
Chan, Garnet Kin-Lic0000-0001-8009-6038
Additional Information:© 2014 John Wiley & Sons, Inc. This work was supported by the Cornell Center for Materials Research, the Center for Molecular Interfacing, NSF CAREER, the Camille and Henry Dreyfus Foundation, the David and Lucile Packard Foundation, and the Alfred P. Sloan Foundation. Claire C. Ralph would like to acknowledge the DOE CSGF program for support.
Funders:
Funding AgencyGrant Number
Cornell Center for Materials ResearchUNSPECIFIED
Center for Molecular InterfacingUNSPECIFIED
NSFUNSPECIFIED
Camille and Henry Dreyfus FoundationUNSPECIFIED
David and Lucile Packard FoundationUNSPECIFIED
Alfred P. Sloan FoundationUNSPECIFIED
Department of Energy (DOE)UNSPECIFIED
Subject Keywords:Green function approach; Hartree–Fock (HF) theory; matrix product states (MPS) approach; random phase approximation (RPA); time evolution
Record Number:CaltechAUTHORS:20170106-121654839
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20170106-121654839
Official Citation:Kinder, J. M., Ralph, C. C. and Kin-Lic Chan, G. (2014) Analytic Time Evolution, Random Phase Approximation, and Green Functions for Matrix Product States, in Quantum Information and Computation for Chemistry: Advances in Chemical Physics Volume 154 (ed S. Kais), John Wiley & Sons, Inc., Hoboken, New Jersey. doi: 10.1002/9781118742631.ch07
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:73299
Collection:CaltechAUTHORS
Deposited By: Donna Wrublewski
Deposited On:06 Jan 2017 20:42
Last Modified:15 Sep 2017 20:31

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