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A theory of minimal updates in holography

Evenbly, G. and Vidal, G. (2015) A theory of minimal updates in holography. Physical Review B, 91 (20). Art. No. 205119. ISSN 1098-0121. doi:10.1103/PhysRevB.91.205119.

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Consider two quantum critical Hamiltonians H and ˜H on a d-dimensional lattice that only differ in some region R. We study the relation between holographic representations, obtained through real-space renormalization, of their corresponding ground states |ψ and |˜ψ. We observe that, even though |ψ and |˜ψ disagree significantly both inside and outside region R, they still admit holographic descriptions that only differ inside the past causal cone C(R) of region R, where C(R) is obtained by coarse-graining region R. We argue that this result follows from a notion of directed influence in the renormalization group flow that is closely connected to the success of Wilson’s numerical renormalization group for impurity problems. At a practical level, directed influence allows us to exploit translation invariance when describing a homogeneous system with, e.g., an impurity, in spite of the fact that the Hamiltonian is no longer invariant under translations.

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Additional Information:© 2015 American Physical Society. Received 27 January 2015; revised manuscript received 22 April 2015; published 20 May 2015. The authors thank Davide Gaiotto, Rob Myers, and Brian Swingle for insightful comments. G.E. is supported by the Sherman Fairchild Foundation. G.V. acknowledges support from the John Templeton Foundation. This research is 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
Sherman Fairchild FoundationUNSPECIFIED
John Templeton FoundationUNSPECIFIED
Perimeter Institute for Theoretical PhysicsUNSPECIFIED
Government of Canada Industry CanadaUNSPECIFIED
Province of Ontario Ministry of Research and InnovationUNSPECIFIED
Issue or Number:20
Classification Code:PACS: 05.30.−d, 02.70.−c, 03.67.Mn, 75.10.Jm
Record Number:CaltechAUTHORS:20140718-123917486
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:47334
Deposited By: Jacquelyn O'Sullivan
Deposited On:20 Jul 2014 22:35
Last Modified:10 Nov 2021 17:38

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