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Deformations of the boundary theory of the square-lattice AKLT model

Martyn, John and Kato, Kohtaro and Lucia, Angelo (2020) Deformations of the boundary theory of the square-lattice AKLT model. Physical Review B, 102 (3). Art. No. 035121. ISSN 2469-9950. doi:10.1103/physrevb.102.035121.

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The one-dimensional (1D) Affleck-Kennedy-Lieb-Tasaki (AKLT) model is a paradigm of antiferromagnetism, and its ground state exhibits symmetry-protected topological order. On a two-dimensional (2D) lattice, the AKLT model has recently gained attention because it too displays symmetry-protected topological order, and its ground state can act as a resource state for measurement-based quantum computation. While the 1D model has been shown to be gapped, it remains an open problem to prove the existence of a spectral gap on the 2D square lattice, which would guarantee the robustness of the resource state. Recently, it has been shown that one can deduce this spectral gap by analyzing the model's boundary theory via a tensor network representation of the ground state. In this work, we express the boundary state of the 2D AKLT model in terms of a classical loop model, where loops, vertices, and crossings are each given a weight. We use numerical techniques to sample configurations of loops and subsequently evaluate the boundary state and boundary Hamiltonian on a square lattice. As a result, we evidence a spectral gap in the square-lattice AKLT model. In addition, by varying the weights of the loops, vertices, and crossings, we indicate the presence of three distinct phases exhibited by the classical loop model.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Kato, Kohtaro0000-0003-3317-2004
Lucia, Angelo0000-0003-1709-1220
Additional Information:© 2020 American Physical Society. Received 15 January 2020; revised 5 June 2020; accepted 23 June 2020; published 10 July 2020. J.M. thanks J. Preskill and C. White for thoughtful discussion. The authors acknowledge support from the Institute for Quantum Information and Matter (IQIM), an NSF Physics Frontiers Center (NSF Grant No. PHY-1733907). We also thank the Caltech SURF program, whose support made this work possible. J.M. is supported by a Southern California Edison WAVE Fellowship. A.L. is supported from the Walter Burke Institute for Theoretical Physics in the form of the Sherman Fairchild Fellowship.
Group:Institute for Quantum Information and Matter, Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
Caltech Summer Undergraduate Research Fellowship (SURF)UNSPECIFIED
Southern California EdisonUNSPECIFIED
Walter Burke Institute for Theoretical Physics, CaltechUNSPECIFIED
Issue or Number:3
Record Number:CaltechAUTHORS:20200710-151322063
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:104338
Deposited By: Tony Diaz
Deposited On:10 Jul 2020 22:31
Last Modified:16 Nov 2021 18:30

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