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Implementation of rigorous renormalization group method for ground space and low-energy states of local Hamiltonians

Roberts, Brenden and Vidick, Thomas and Motrunich, Olexei I. (2017) Implementation of rigorous renormalization group method for ground space and low-energy states of local Hamiltonians. Physical Review B, 96 (21). Art. No. 214203. ISSN 2469-9950. http://resolver.caltech.edu/CaltechAUTHORS:20170627-090122309

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Abstract

The success of polynomial-time tensor network methods for computing ground states of certain quantum local Hamiltonians has recently been given a sound theoretical basis by Arad et al. [Math. Phys. 356, 65 (2017)]. The convergence proof, however, relies on “rigorous renormalization group” (RRG) techniques which differ fundamentally from existing algorithms. We introduce a practical adaptation of the RRG procedure which, while no longer theoretically guaranteed to converge, finds matrix product state ansatz approximations to the ground spaces and low-lying excited spectra of local Hamiltonians in realistic situations. In contrast to other schemes, RRG does not utilize variational methods on tensor networks. Rather, it operates on subsets of the system Hilbert space by constructing approximations to the global ground space in a treelike manner. We evaluate the algorithm numerically, finding similar performance to density matrix renormalization group (DMRG) in the case of a gapped nondegenerate Hamiltonian. Even in challenging situations of criticality, large ground-state degeneracy, or long-range entanglement, RRG remains able to identify candidate states having large overlap with ground and low-energy eigenstates, outperforming DMRG in some cases.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1103/PhysRevB.96.214203DOIArticle
https://journals.aps.org/prb/abstract/10.1103/PhysRevB.96.214203PublisherArticle
https://arxiv.org/abs/1703.01994arXivDiscussion Paper
ORCID:
AuthorORCID
Vidick, Thomas0000-0002-6405-365X
Motrunich, Olexei I.0000-0001-8031-0022
Alternate Title:Rigorous renormalization group method for ground space and low-energy states of local Hamiltonians
Additional Information:© 2017 American Physical Society. Received 2 April 2017; published 18 December 2017. We acknowledge useful discussions with M. Fishman and S. White's research group, as well as with C. White and C.-J. Lin. The numerical results were computed with the ITensor library [20] of E. Stoudenmire and S. White. This work was supported by the Institute for Quantum Information and Matter, an NSF Physics Frontiers Center, with support of the Gordon and Betty Moore Foundation. Additional funding support was provided by the NSF through Grant No. DMR-1619696.
Group:IQIM, Institute for Quantum Information and Matter
Funders:
Funding AgencyGrant Number
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
NSF Physics Frontiers CenterUNSPECIFIED
Gordon and Betty Moore FoundationUNSPECIFIED
NSFDMR-1619696
Record Number:CaltechAUTHORS:20170627-090122309
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20170627-090122309
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:78597
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:27 Jun 2017 16:39
Last Modified:14 Jun 2018 20:46

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