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Fracton phases via exotic higher-form symmetry-breaking

Oct 5, 2020

21 pages

Published in:

Annals Phys. 424 (2021) 168360

Published: Nov 26, 2020
and
Published: Jan, 2021

e-Print:

2010.02254 [cond-mat.str-el]

DOI:

10.1016/j.aop.2020.168360 (publication)

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Abstract: (Elsevier Inc.)

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.

Note:

21 pages, 7 figures. v2: final published version, minor changes from v1

Fracton phases
Higher symmetry
model: lattice
charge: scalar
field theory: scalar
condensation
symmetry breaking
homology
fractional
string

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