Addendum: Area law violations and quantum phase transitions in modified Motzkin walk spin chains

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Title
Addendum: Area law violations and quantum phase transitions in modified Motzkin walk spin chains
Author(s)
Fumihiko Sugino; Pramod Padmanabhan
Publication Date
2018-05
Journal
JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT, v.2018, no.1, pp.013101 -
Publisher
IOP PUBLISHING LTD
Abstract
Area law violations for entanglement entropy in the form of a square root has recently been studied for one-dimensional frustration-free quantum systems based on the Motzkin walks and their variations. Here we consider a Motzkin walk with a different Hilbert space on each step of the walk spanned by elements of a {\it Symmetric Inverse Semigroup} with the direction of each step governed by its algebraic structure. This change alters the number of paths allowed in the Motzkin walk and introduces a ground state degeneracy sensitive to boundary perturbations. We study the frustration-free spin chains based on three symmetric inverse semigroups, S-1(3), S-2(3), and S-1(2),The system based on S-1(3) and S-2(3) provide examples of quantum phase transitions in one dimensions with the former exhibiting a transition between the area law and a logarithmic violation of the area law and the latter providing an example of transition from logarithmic scaling to a square root scaling in the system size, mimicking a colored S-1(3) system. The system with S-1(2) is much simpler and produces states that continue to obey the area law. © 2018 The Author(s). Published by IOP Publishing Ltd on behalf of SISSA Medialab srl
URI
https://pr.ibs.re.kr/handle/8788114/4532
ISSN
1742-5468
Appears in Collections:
Center for Fundamental Theory(순수물리이론 연구단) > Journal Papers (저널논문)
Center for Theoretical Physics of Complex Systems(복잡계 이론물리 연구단) > Journal Papers (저널논문)
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