Classification of 1+1D gapless symmetry protected phases via topological
holography
- URL: http://arxiv.org/abs/2311.00050v1
- Date: Tue, 31 Oct 2023 18:02:01 GMT
- Title: Classification of 1+1D gapless symmetry protected phases via topological
holography
- Authors: Rui Wen and Andrew C. Potter
- Abstract summary: We establish a one-to-one correspondence between 1+1D bosonic gSPTs, and partially-confined boundaries of 2+1D SymTFTs.
We show that this data precisely matches that of symmetry-preserving partial confinement (or partially gapped boundaries) of 2+1D quantum double models.
- Score: 1.6528578738461073
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Symmetry topological field theory (SymTFT) gives a holographic correspondence
between systems with a global symmetry and a higher-dimensional topological
field theory. In this framework, classification of gapped phases of matter in
spacetime dimension 1+1D correspond to classifications of mechanisms to confine
the SymTFT by condensing anyons. In this work, we extend these results to
characterize gapless symmetry-protected topological states: symmetry-enriched
gapless phases or critical points that exhibit edge modes protected by symmetry
and topology. We establish a one-to-one correspondence between 1+1D bosonic
gSPTs, and partially-confined boundaries of 2+1D SymTFTs. From general physical
considerations, we determine the set of data and consistency conditions
required to define a 1+1D gSPT, and show that this data precisely matches that
of symmetry-preserving partial confinement (or partially gapped boundaries) of
2+1D quantum double models. We illustrate this correspondence through a
dimensional reduction (thin-slab) construction, which enables a
physically-intuitive derivation of how properties of the gSPT such as edge
modes, emergent anomalies, and stability to perturbations arise from the SymTFT
perspective.ditions required to define a 1+1D gSPT and show that they fully
determine the physics of the gSPT including edge modes and emergent anomaly.
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