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A simplified and improved approach to tensor network operators in two dimensions

O'Rourke, Matthew J. and Chan, Garnet Kin-Lic (2020) A simplified and improved approach to tensor network operators in two dimensions. Physical Review B, 101 (20). Art. No. 205142. ISSN 2469-9950.

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Matrix product states and matrix product operators (MPOs) are one-dimensional tensor networks that underlie the modern density matrix renormalization group (DMRG) algorithm. The use of MPOs accounts for the high level of generality and wide range of applicability of DMRG. However, current algorithms for two-dimensional (2D) tensor network states, known as projected entangled-pair states, rarely employ the associated 2D tensor network operators, projected entangled-pair operators (PEPOs), due to their computational cost and conceptual complexity. To lower these two barriers, we describe how to reformulate a PEPO into a set of tensor network operators that resemble MPOs by considering the different sets of local operators that are generated from sequential bipartitions of the 2D system. The expectation value of a PEPO can then be evaluated on the fly using only the action of MPOs and generalized MPOs at each step of the approximate contraction of the 2D tensor network. This technique allows for the simpler construction and more efficient energy evaluation of 2D Hamiltonians that contain finite-range interactions, and provides an improved strategy to encode long-range interactions that is orders of magnitude more accurate and efficient than existing schemes.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
O'Rourke, Matthew J.0000-0002-5779-2577
Chan, Garnet Kin-Lic0000-0001-8009-6038
Additional Information:© 2020 American Physical Society. Received 11 November 2019; revised manuscript received 12 March 2020; accepted 6 April 2020; published 22 May 2020. Primary support for this work was from AFOSR MURI Grant No. FA9550-18-1-0095. M.J.O. acknowledges financial support from a US National Science Foundation Graduate Research Fellowship via Grant No. DEG-1745301. G.K.C. acknowledges support from the Simons Foundation. The authors thank H. Schurkus and Z. Li for helpful feedback on the manuscript.
Funding AgencyGrant Number
Air Force Office of Scientific Research (AFOSR)FA9550-18-1-0095
NSF Graduate Research FellowshipDEG-1745301
Simons FoundationUNSPECIFIED
Issue or Number:20
Record Number:CaltechAUTHORS:20191218-113037284
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:100349
Deposited By: Tony Diaz
Deposited On:18 Dec 2019 19:34
Last Modified:22 May 2020 17:24

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