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Unified structure for exact towers of scar states in the AKLT and other models

Mark, Daniel K. and Lin, Cheng-Ju and Motrunich, Olexei I. (2020) Unified structure for exact towers of scar states in the AKLT and other models. . (Unpublished)

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Quantum many-body scar states are many-body states with finite energy density in non-integrable models that do not obey the eigenstate thermalization hypothesis. Recent works have revealed "towers" of scar states that are exactly known and are equally spaced in energy, specifically in the AKLT model, the spin-1 XY model, and a spin-1/2 model that conserves number of domain walls. We provide a common framework to understand and prove known exact towers of scars in these systems, by evaluating the commutator of the Hamiltonian and a ladder operator. In particular we provide a simple proof of the scar towers in the integer-spin 1d AKLT models by studying two-site spin projectors. Through this picture we deduce a family of Hamiltonians that share the scar tower with the AKLT model, and also find common parent Hamiltonians for the AKLT and XY model scars. We also introduce new towers of exact states, organized in a "pyramid" structure, in the spin-1/2 model through successive application of a non-local ladder operator.

Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription Paper
Lin, Cheng-Ju0000-0001-7898-0211
Motrunich, Olexei I.0000-0001-8031-0022
Additional Information:We thank Alvaro Alhambra, Anushya Chandran, Timothy Hsieh, Rahul Nandkishore, Tibor Rakovszky, and Christopher Turner for valuable discussions. We also thank Andrei Bernevig, Juan P. Garrahan, Thomas Iadecola, Hosho Katsura, Sanjay Moudgalya, Zlatko Papić, and Nicolas Regnault for comments and discussions on the manuscript. D. M. acknowledges funding from the James C. Whitney SURF Fellowship, Caltech Student-Faculty Programs. This work was also supported by National Science Foundation through Grant DMR-1619696. C.-J. L. acknowledges support from Perimeter Institute for Theoretical Physics. Research at Perimeter Institute is supported in part by the Government of Canada through the Department of Innovation, Science and Economic Development Canada and by the Province of Ontario through the Ministry of Economic Development, Job Creation and Trade.
Funding AgencyGrant Number
Caltech Summer Undergraduate Research Fellowship (SURF)UNSPECIFIED
Perimeter Institute for Theoretical PhysicsUNSPECIFIED
Department of Innovation, Science and Economic Development (Canada)UNSPECIFIED
Ontario Ministry of Economic Development, Job Creation and TradeUNSPECIFIED
Record Number:CaltechAUTHORS:20200303-083407096
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:101673
Deposited By: Tony Diaz
Deposited On:03 Mar 2020 18:43
Last Modified:03 Mar 2020 18:43

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