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Faster methods for contracting infinite two-dimensional tensor networks

Fishman, M. T. and Vanderstraeten, L. and Zauner-Stauber, V. and Haegeman, J. and Verstraete, F. (2018) Faster methods for contracting infinite two-dimensional tensor networks. Physical Review B, 98 (23). Art. No. 235148. ISSN 2469-9950. doi:10.1103/physrevb.98.235148.

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We revisit the corner transfer matrix renormalization group (CTMRG) method of Nishino and Okunishi for contracting two-dimensional (2D) tensor networks and demonstrate that its performance can be substantially improved by determining the tensors using an eigenvalue solver as opposed to the power method used in CTMRG. We also generalize the variational uniform matrix product state (VUMPS) ansatz for diagonalizing 1D quantum Hamiltonians to the case of 2D transfer matrices and discuss similarities with the corner methods. These two new algorithms will be crucial to improving the performance of variational infinite projected entangled pair state (PEPS) methods.

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Alternate Title:Faster Methods for Contracting Infinite 2D Tensor Networks
Additional Information:© 2018 American Physical Society. Received 27 October 2018; revised manuscript received 1 December 2018; published 26 December 2018. M.F. acknowledges helpful feedback from P. R. Corboz and T. Nishino. M. F. would also like to thank S. R. White and E. M. Stoudenmire for useful input on the presentation of the results. The authors gratefully acknowledge support from the National Science Foundation Graduate Research Fellowship Program (NSF GRFP) under Grant No. DGE-1144469 (M.F.), the Austrian Science Fund (FWF): F4104 SFB ViCoM and F4014 SFB FoQuS (V.Z.-S. and F.V.), and the European Research Council (ERC) under Grant No. 715861 (J.H.). J.H. and L.V. are supported by the Research Foundation Flanders (FWO). This project has received funding from the European Research Council (ERC) under the European Unions Horizon 2020 research and innovation programme (Grant Agreement No. 647905). This work used the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation Grant No. ACI-1548562.
Group:Institute for Quantum Information and Matter
Funding AgencyGrant Number
NSF Graduate Research FellowshipDGE-1144469
FWF Der WissenschaftsfondsF4104 SFB ViCoM
FWF Der WissenschaftsfondsF4014 SFB FoQuS
European Research Council (ERC)715861
Fonds Wetenschappelijk Onderzoek (FWO)UNSPECIFIED
European Research Council (ERC)647905
Issue or Number:23
Record Number:CaltechAUTHORS:20180626-152653715
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:87361
Deposited By: Tony Diaz
Deposited On:26 Jun 2018 22:40
Last Modified:15 Nov 2021 20:47

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