Noninvertible Symmetry-Protected Topological Order in a Group-Based Cluster State

IF 11.6 1区物理与天体物理 Q1 PHYSICS, MULTIDISCIPLINARY

Physical Review X Pub Date : 2025-03-13 DOI:10.1103/physrevx.15.011058

Christopher Fechisin, Nathanan Tantivasadakarn, Victor V. Albert

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引用次数: 0

Abstract

Despite growing interest in beyond-group symmetries in quantum condensed matter systems, there are relatively few microscopic lattice models explicitly realizing these symmetries, and many phenomena have yet to be studied at the microscopic level. We introduce a one-dimensional stabilizer Hamiltonian composed of group-based Pauli operators whose ground state is a G×Rep(G)-symmetric state: the G-cluster state introduced by Brell []. We show that this state lies in a symmetry-protected topological (SPT) phase protected by G×Rep(G) symmetry, distinct from the symmetric product state by a duality argument. We identify several signatures of SPT order, namely, protected edge modes, string order parameters, and topological response. We discuss how G-cluster states may be used as a universal resource for measurement-based quantum computation, explicitly working out the case where G is a semidirect product of Abelian groups.

Published by the American Physical Society

2025

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来源期刊

Physical Review X PHYSICS, MULTIDISCIPLINARY-

CiteScore

24.60

自引率

1.60%

发文量

197

审稿时长

3 months

期刊介绍： Physical Review X (PRX) stands as an exclusively online, fully open-access journal, emphasizing innovation, quality, and enduring impact in the scientific content it disseminates. Devoted to showcasing a curated selection of papers from pure, applied, and interdisciplinary physics, PRX aims to feature work with the potential to shape current and future research while leaving a lasting and profound impact in their respective fields. Encompassing the entire spectrum of physics subject areas, PRX places a special focus on groundbreaking interdisciplinary research with broad-reaching influence.