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It has recently been understood that the complete global symmetry of finite group topological gauge theories contains the structure of a higher-group. Here we study the higher-group structure in (3+1)D\mathbb{Z}_2 gauge theory with an emergent fermion, and point out that pumping chiralp+ip topological states gives rise to a\mathbb{Z}_{8} 0-form symmetry with mixed gravitational anomaly. This ordinary symmetry mixes with the other higher symmetries to form a 3-group structure, which we examine in detail. We then show that in the context of stabilizer quantum codes, one can obtain logical CCZ and CS gates by placing the code on a discretization ofT^3 (3-torus) andT^2 \rtimes_{C_2} S^1 (2-torus bundle over the circle) respectively, and pumpingp+ip states. Our considerations also imply the possibility of a logicalT gate by placing the code on\mathbb{RP}^3 and pumping ap+ip topological state.
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Pumping with symmetry
Abstract Re-configurable materials and meta-materials can jump between space symmetry classes during their deformations. Here, we introduce the concept of singular symmetry enhancement, which refers to an abrupt jump to a higher symmetry class accompanied by an un-avoidable reduction in the number of dispersion bands of the excitations of the material. Such phenomenon prompts closings of some of the spectral resonant gaps along singular manifolds in a parameter space. In this work, we demonstrate that these singular manifolds can carry topological charges. As a concrete example, we show that a deformation of an acoustic crystal that encircles aconfiguration of an array of cavity resonators results in an adiabatic cycle that carries a Chern number in the bulk and displays Thouless pumping at the edges. This points to a very general guiding principle for recognizing cyclic adiabatic processes with high potential for topological pumping in complex materials and meta-materials, which rests entirely on symmetry arguments.
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- PAR ID:
- 10555584
- Publisher / Repository:
- EPS
- Date Published:
- Journal Name:
- Europhysics Letters
- Volume:
- 146
- Issue:
- 1
- ISSN:
- 0295-5075
- Page Range / eLocation ID:
- 16004
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1209/0295-5075/ad3053
