Conflicting Symmetries in Topologically Ordered Surface States of Three-dimensional Bosonic Symmetry Protected Topological Phases

Gil Young Cho; Jeffrey C. Teo; Shinsei Ryu

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Conflicting Symmetries in Topologically Ordered Surface States of Three-dimensional Bosonic Symmetry Protected Topological Phases

Gil Young Cho, Jeffrey C. Teo, Shinsei Ryu

Strongly Correlated Electrons · Submitted 9 Mar 2014

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Given that there is no such phenomena in the purely two-dimensional model, it signals that the symmetries are encoded anomalously on the surface of the three-dimensional SPT phases and that the surface state can never be realized on the purely two-dimensional models.

how it is stated · asserted 0.85 read the record →

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arXiv ID1403.2018 (version 2)

Pith ID4A5BT26J, Pith's permanent record of this paper and its review

CitationGil Young Cho, Jeffrey C. Teo, Shinsei Ryu. "Conflicting Symmetries in Topologically Ordered Surface States of Three-dimensional Bosonic Symmetry Protected Topological Phases." arXiv:1403.2018 (2014). https://pith.science/paper/4A5BT26J

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What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.29 · human participants 0.01 · controlled comparison 0.13 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.71 · mentions code or data availability 0.01.

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arXiv listing abstract v2. Results and the main claim are underlined; show every role.

We study the Z2 topologically ordered surface state of three-dimensional bosonic SPT phases with the discrete symmetries G1 x G2. It has been argued that the topologically ordered surface state cannot be realized on a purely two-dimensional lattice model. We carefully examine the statement and show that the surface state should break G2 if the symmetry G1 is gauged. This manifests the conflict of the symmetry G1 and G2 on the surface of the three-dimensional SPT phase. Given that there is no such phenomena in the purely two-dimensional model, it signals that the symmetries are encoded anomalously on the surface of the three-dimensional SPT phases and that the surface state can never be realized on the purely two-dimensional models.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We study the Z2 topologically ordered surface state of three-dimensional bosonic SPT phases with the discrete symmetries G1 x G2.	contribution 0.87	0.80	0.03	asserted 0.83
s1	It has been argued that the topologically ordered surface state cannot be realized on a purely two-dimensional lattice model.	background 0.99	0.03	0.06	asserted 0.78
s2	We carefully examine the statement and show that the surface state should break G2 if the symmetry G1 is gauged.	result 0.95	0.91	0.64	asserted 0.99
s3	This manifests the conflict of the symmetry G1 and G2 on the surface of the three-dimensional SPT phase.	interpretation 0.94	0.59	0.29	asserted 0.99
s4	Given that there is no such phenomena in the purely two-dimensional model, it signals that the symmetries are encoded anomalously on the surface of the three-dimensional SPT phases and that the surface state can never be realized on the purely two-dimensional models.	interpretation 0.99	0.49	0.77	asserted 0.85

What kind of paper the classifier reports this is: theoretical result 0.97 · evidence from argument 0.83.

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Original abstract

We study the Z2 topologically ordered surface state of three-dimensional bosonic SPT phases with the discrete symmetries G1 x G2. It has been argued that the topologically ordered surface state cannot be realized on a purely two-dimensional lattice model. We carefully examine the statement and show that the surface state should break G2 if the symmetry G1 is gauged. This manifests the conflict of the symmetry G1 and G2 on the surface of the three-dimensional SPT phase. Given that there is no such phenomena in the purely two-dimensional model, it signals that the symmetries are encoded anomalously on the surface of the three-dimensional SPT phases and that the surface state can never be realized on the purely two-dimensional models.

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References

Forward citations

Cited by 12 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

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27 arXiv papers cite this in 32 sentences

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Builds on it 1 paper

We further extend these ideas to construct fixed-point wave functions for anomalous surface topological orders of 3D SPT phases described by group cohomology models [ref] .

Exactly Solvable Models for Symmetry-Enriched Topological Phases · Introduction · 0.87

Cites it as background 9 papers

Thanks to theoretical developments of symmetry-protected topological (SPT) phases, we now obtain much deep understandings of anomaly matching condition [ref] (see, for example, Refs. [ref] for some of recent applications).

Sigma-model analysis of $SU(3)$ antiferromagnetic spins on the triangular lattice · Phase transition and constraints by anomaly matching · 0.90
Indeed, the phase diagram of the QCD(BF) has been investigated from the anomaly matching as well as from some calculable limits [ref] (See also Refs. [ref] for recent developments of anomaly matching and global inconsistency), and these studies uncover its nontrivial phase diagram.

Non-supersymmetric duality cascade of QCD(BF) via semiclassics on $\mathbb{R}^2\times T^2$ with the baryon-'t Hooft flux · Introduction and Summary · 0.82
Thanks to the development of symmetry-protected topological phases [ref] , people understand that the applicability of 't Hooft anomaly matching condition is much broader, and anomaly matching conditions are providing new insights on strongly-coupled QFTs [ref] .

High-temperature domain walls of QCD with imaginary chemical potentials · Introduction · 0.80

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Uses the method or tool of 1 paper

As before, we begin with identifying a new anyon excitation $l_v$ in the charge lattice [ref] . l⃗_v = K δϕ⃗/2π = (0,0,0,1/2)^T,

Classification and Properties of Symmetry Enriched Topological Phases: A Chern-Simons approach with applications to Z2 spin liquids · $ℤ^A_2 ×ℤ^B_2 ×ℤ^C_2$ symmetric case · 0.89

Cites as background 7 papers

It has been shown that the three-dimensional bosonic SPT phases can be successfully studied by the semi-classical O(5) non-linear sigma model supplemented by the topological $Θ$-term [ref] .

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As before we assume $G_1$ is “conventional” [ref] and shifts the phases of the quasi-particle excitations.

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The other quantum disordered states, which has been studied extensively recently, are so-called a Symmetry Protected Topological (SPT) phase [ref] .

Quantum phase transitions between bosonic symmetry protected topological phases in two dimensions: emergent $QED_3$ and anyon superfluid · Introduction · 0.90

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