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Conversion of projected entangled pair states into a canonical form

Haghshenas, Reza and O'Rourke, Matthew J. and Chan, Garnet Kin-Lic (2019) Conversion of projected entangled pair states into a canonical form. Physical Review B, 100 (5). Art. No. 054404. ISSN 2469-9950. http://resolver.caltech.edu/CaltechAUTHORS:20190513-130649313

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Abstract

We propose an algorithm to convert a projected entangled pair state (PEPS) into a canonical form, analogous to the well-known canonical form of a matrix product state. Our approach is based on a variational gauging ansatz for the QR tensor decomposition of PEPS columns into a matrix product operator and a finite depth circuit of unitaries and isometries. We describe a practical initialization scheme that leads to rapid convergence in the QR optimization. We explore the performance and stability of the variational gauging algorithm in norm calculations for the transverse-field Ising and Heisenberg models on a square lattice. We also demonstrate energy optimization within the PEPS canonical form for the transverse-field Ising and Heisenberg models. We expect this canonical form to open up improved analytical and numerical approaches for PEPS.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1103/PhysRevB.100.054404DOIArticle
https://arxiv.org/abs/1903.03843arXivDiscussion Paper
ORCID:
AuthorORCID
Haghshenas, Reza0000-0002-5593-8915
Chan, Garnet Kin-Lic0000-0001-8009-6038
Alternate Title:Canonicalization of projected entangled pair states
Additional Information:© 2019 American Physical Society. Received 14 March 2019; revised manuscript received 18 July 2019; published 5 August 2019. Primary support for this work was from MURI FA9550-18-1-0095. Some of the code used to test energy optimization was based on work supported by the US National Science Foundation (NSF) via Grant No. CHE-1665333. M.J.O. acknowledges a US NSF Graduate Research Fellowship via Grant No. DEG-1745301. G.K.C. acknowledges support from the Simons Foundation. We have used Uni10 [39] as a middleware library to build the variational gauging ansatz.
Funders:
Funding AgencyGrant Number
Air Force Office of Scientific Research (AFOSR)FA9550-18-1-0095
NSFCHE-1665333
NSF Graduate Research FellowshipDGE-1745301
Simons FoundationUNSPECIFIED
Issue or Number:5
Record Number:CaltechAUTHORS:20190513-130649313
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20190513-130649313
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:95436
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:13 May 2019 20:10
Last Modified:09 Aug 2019 20:58

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