Classification of dipolar symmetry-protected topological phases: Matrix product states, stabilizer Hamiltonians, and finite tensor gauge theories

Lam, Ho Tat

doi:10.1103/physrevb.109.115142

Phys. Rev. B

2024

DOI: 10.1103/physrevb.109.115142

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Classification of dipolar symmetry-protected topological phases: Matrix product states, stabilizer Hamiltonians, and finite tensor gauge theories

Ho Tat Lam

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2024

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Cited by 4 publications

References 124 publications

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Anomaly inflow for dipole symmetry and higher form foliated field theories

Ebisu,

Honda,

Nakanishi

2024

J. High Energ. Phys.

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In accordance with recent progress of fracton topological phases, unusual topological phases of matter hosting fractionalized quasiparticle excitations with mobility constraints, new type of symmetry is studied — multipole symmetry, associated with conservation of multipoles. Based on algebraic relation between dipole and global charges, we introduce a series of (d + 1)-dimensional BF theories with p-form gauge fields, which admit dipole of spatially extended excitations, and study their physical properties. We elucidate that gauge invariant loops have unusual form, containing linear function of the spatial coordinate, which leads to the position dependent braiding statistics and unusual ground state degeneracy dependence on the system size. We also show that the theories exhibit a mixed ’t Hooft anomaly between p-form and (d − p)-form dipole symmetries, which is canceled by an invertible theory defined in one dimensional higher via anomaly inflow mechanism.

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Anomaly inflow for dipole symmetry and higher form foliated field theories

Ebisu,

Honda,

Nakanishi

2024

J. High Energ. Phys.

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Higher-order topological phase with subsystem symmetries

You

2024

New J. Phys.

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A wide variety of higher-order symmetry-protected topological phases (HOSPT) with gapless corners or hinges have been proposed as descendants of topological crystalline insulators protected by spatial symmetry. In this work, we address a new class of higher-order topological states that do not require crystalline symmetries but instead rely on subsystem symmetry for protection. We propose several strongly interacting models with gapless hinges or corners based on a decorated hinge-wall condensate picture. The hinge-wall, which appears as the defect configuration of a Z 2 paramagnet, is decorated with a lower-dimensional SPT state. Such a unique hinge-wall decoration structure leads to gapped surfaces separated by gapless hinges. The non-trivial nature of the hinge modes can be captured by a 1 + 1 D conformal field theory with a Wess–Zumino–Witten term. Moreover, we establish a no-go theorem to demonstrate the ungappable nature of the hinges by making a connection between the generalized Lieb–Schultz–Mattis theorem and the boundary anomaly of the HOSPT state. This universal correspondence engenders a comprehensive criterion to determine the existence of HOSPT under certain symmetries, regardless of the microscopic Hamiltonian.

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Generating lattice non-invertible symmetries

Cao,

Li,

Yamazaki

2024

SciPost Phys.

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Lattice non-invertible symmetries have rich fusion structures and play important roles in understanding various exotic topological phases. In this paper, we explore methods to generate new lattice non-invertible transformations/symmetries from a given non-invertible seed transformation/symmetry. The new lattice non-invertible symmetry is constructed by composing the seed transformations on different sites or sandwiching a unitary transformation between the transformations on the same sites. In addition to known non-invertible symmetries with fusion algebras of Tambara-Yamagami \mathbb Z_N×\mathbb Z_NℤN×ℤN type, we obtain a new non-invertible symmetry in models with \mathbb Z_NℤN dipole symmetries. We name the latter the dipole Kramers-Wannier symmetry because it arises from gauging the dipole symmetry. We further study the dipole Kramers-Wannier symmetry in depth, including its topological defect, its anomaly and its associated generalized Kennedy-Tasaki transformation.

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Classification of dipolar symmetry-protected topological phases: Matrix product states, stabilizer Hamiltonians, and finite tensor gauge theories

Cited by 4 publications

References 124 publications

Anomaly inflow for dipole symmetry and higher form foliated field theories

Anomaly inflow for dipole symmetry and higher form foliated field theories

Higher-order topological phase with subsystem symmetries

Generating lattice non-invertible symmetries

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