Systematic construction of gapped nonliquid states
Name
PhysRevResearch.2.033300.pdf
Description
Published version
Size
750.91 KB
Format
Adobe PDF
Checksum (MD5)
41399652acbdfa8ecd4430be3186072a
Author(s)
Wen, Xiao-Gang
Date Issued
2020
Journal
Physical Review Research
Publisher
American Physical Society (APS)
Version
Final published version
Abstract
Gapped non-liquid state (also known as fracton state) is a very special
gapped quantum state of matter that is characterized by a microscopic cellular
structure. Such microscopic cellular structure has a macroscopic effect at
arbitrary long distances and cannot be removed by renormalization group flow,
which makes gapped non-liquid state beyond the description of topological
quantum field theory with a finite number of fields. Using Abelian and
non-Abelian topological orders in 2-dimensional (2d) space and the different
ways to glue them together via their gapped boundaries, we propose a systematic
way to construct 3d gapped states (and in other dimensions). The resulting
states are called cellular topological states, which include gapped non-liquid
states, as well as gapped liquid states in some special cases. Some new fracton
states with fractal excitations are constructed even using 2d $\mathbb{Z}_2$
topological order. More general cellular topological states can be constructed
by connecting 2d domain walls between different 3d topological orders. The
constructed cellular topological states can be viewed as fixed-point states for
a reverse renormalization of gapped non-liquid states.
MIT Department
Massachusetts Institute of Technology. Department of Physics
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Creative Commons Attribution 4.0 International license
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DOI of Published Version
https://doi.org/10.1103/physrevresearch.2.033300
