Fracton phases via exotic higher-form symmetry-breaking

• URL: http://arxiv.org/abs/2010.02254v2
• Date: Sat, 2 Jan 2021 18:43:48 GMT
• Title: Fracton phases via exotic higher-form symmetry-breaking
• Authors: Marvin Qi, Leo Radzihovsky, Michael Hermele
• Abstract summary: We study p-string condensation mechanisms for fracton phases from the viewpoint of higher-form symmetry. We focus on the examples of the X-cube model and the rank-two symmetric-tensor U(1) scalar charge theory.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study p-string condensation mechanisms for fracton phases from the viewpoint of higher-form symmetry, focusing on the examples of the X-cube model and the rank-two symmetric-tensor U(1) scalar charge theory. This work is motivated by questions of the relationship between fracton phases and continuum quantum field theories, and also provides general principles to describe p-string condensation independent of specific lattice model constructions. We give a perspective on higher-form symmetry in lattice models in terms of cellular homology. Applying this perspective to the coupled-layer construction of the X-cube model, we identify a foliated 1-form symmetry that is broken in the X-cube phase, but preserved in the phase of decoupled toric code layers. Similar considerations for the scalar charge theory lead to a framed 1-form symmetry. These symmetries are distinct from standard 1-form symmetries that arise, for instance, in relativistic quantum field theory. We also give a general discussion on interpreting p-string condensation, and related constructions involving gauging of symmetry, in terms of higher-form symmetry.

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