TY - JOUR
T1 - Noninvertible Symmetry-Protected Topological Order in a Group-Based Cluster State
AU - Fechisin, Christopher
AU - Tantivasadakarn, Nathanan
AU - Albert, Victor V.
N1 - Publisher Copyright:
© 2025 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the "https://creativecommons.org/licenses/by/4.0/"Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.
PY - 2025/1
Y1 - 2025/1
N2 - 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 [New J. Phys. 17, 023029 (2015)NJOPFM1367-263010.1088/1367-2630/17/2/023029]. 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.
AB - 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 [New J. Phys. 17, 023029 (2015)NJOPFM1367-263010.1088/1367-2630/17/2/023029]. 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.
UR - https://www.scopus.com/pages/publications/105001104075
U2 - 10.1103/PhysRevX.15.011058
DO - 10.1103/PhysRevX.15.011058
M3 - Article
AN - SCOPUS:105001104075
SN - 2160-3308
VL - 15
JO - Physical Review X
JF - Physical Review X
IS - 1
M1 - 011058
ER -