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Variational optimization algorithms for uniform matrix product states

Zauner-Stauber, V. and Vanderstraeten, L. and Fishman, M.T. and Verstraete, F. and Haegeman, J. (2018) Variational optimization algorithms for uniform matrix product states. Physical Review B, 97 (4). Art. No. 045145. ISSN 2469-9950. doi:10.1103/PhysRevB.97.045145.

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We combine the density matrix renormalization group (DMRG) with matrix product state tangent space concepts to construct a variational algorithm for finding ground states of one-dimensional quantum lattices in the thermodynamic limit. A careful comparison of this variational uniform matrix product state algorithm (VUMPS) with infinite density matrix renormalization group (IDMRG) and with infinite time evolving block decimation (ITEBD) reveals substantial gains in convergence speed and precision. We also demonstrate that VUMPS works very efficiently for Hamiltonians with long-range interactions and also for the simulation of two-dimensional models on infinite cylinders. The new algorithm can be conveniently implemented as an extension of an already existing DMRG implementation.

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Additional Information:© 2018 Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Received 9 March 2017; revised manuscript received 10 December 2017; published 25 January 2018. The authors acknowledge inspiring and insightful discussions with M. Ganahl, M. Mariën, and I. P. McCulloch. We thank B. Buyens for providing templates for drawing tensor network diagrams. We also thank J. Osorio Iregui for providing IDMRG data for infinite cylinder simulations. This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No. 647905). The authors gratefully acknowledge support from the Austrian Science Fund (FWF): F4104 SFB ViCoM and F4014 SFB FoQuS (V.Z.-S. and F.V.), and GRW 1-N36 (M.F.). J.H. and L.V. are supported by the Research Foundation Flanders (FWO).
Group:Institute for Quantum Information and Matter
Funding AgencyGrant Number
European Research Council (ERC)647905
FWF Der WissenschaftsfondsF4104 SFB ViCoM
FWF Der WissenschaftsfondsF4014 SFB FoQuS
FWF Der WissenschaftsfondsGRW 1-N36
Fonds voor Wetenschappelijk Onderzoek (FWO)UNSPECIFIED
Issue or Number:4
Record Number:CaltechAUTHORS:20171103-134852714
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:82942
Deposited By: Bonnie Leung
Deposited On:07 Nov 2017 02:42
Last Modified:15 Nov 2021 19:54

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