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Algorithms for entanglement renormalization: boundaries, impurities and interfaces

Evenbly, Glen and Vidal, Guifré (2014) Algorithms for entanglement renormalization: boundaries, impurities and interfaces. Journal of Statistical Physics, 157 (4-5). pp. 931-978. ISSN 0022-4715. doi:10.1007/s10955-014-0983-1.

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We propose algorithms, based on the multi-scale entanglement renormalization ansatz, to obtain the ground state of quantum critical systems in the presence of boundaries, impurities, or interfaces. By exploiting the theory of minimal updates [G. Evenbly and G. Vidal, arXiv:1307.0831], the ground state is completely characterized in terms of a number of variational parameters that is independent of the system size, even though the presence of a boundary, an impurity, or an interface explicitly breaks the translation invariance of the host system. Similarly, computational costs do not scale with the system size, allowing the thermodynamic limit to be studied directly and thus avoiding finite size effects e.g. when extracting the universal properties of the critical system.

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Additional Information:© 2014 Springer Science+Business Media New York. Received: 5 March 2014; Accepted: 21 March 2014; Published online: 22 April 2014. The authors acknowledge Kouichi Okunishi for helpful discussions regarding Wilson’s solution to the Kondo problem, and helpful input from Masaki Oshikawa regarding the two-impurity Ising model. Support from the Australian Research Council (APA, FF0668731, DP0878830) is acknowledged. G.E. is supported by the Sherman Fairchild foundation. This research was supported in part by Perimeter Institute for Theoretical Physics. Research at Perimeter Institute is supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Research and Innovation.
Group:Institute for Quantum Information and Matter
Funding AgencyGrant Number
Australian Research CouncilFF0668731
Australian Research CouncilDP0878830
Sherman Fairchild FoundationUNSPECIFIED
Perimeter Institute for Theoretical PhysicsUNSPECIFIED
Issue or Number:4-5
Classification Code:PACS numbers: 05.30.-d, 02.70.-c, 03.67.Mn, 05.50.+q
Record Number:CaltechAUTHORS:20140718-142700398
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Official Citation:Evenbly, G. & Vidal, G. J Stat Phys (2014) 157: 931. doi:10.1007/s10955-014-0983-1
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:47342
Deposited By: Jacquelyn O'Sullivan
Deposited On:20 Jul 2014 22:59
Last Modified:10 Nov 2021 17:38

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