Gapped Symmetry Preserving Surface-State for the Electron Topological Insulator

Andrew C. Potter; Chong Wang; T. Senthil

RECORD

Gapped Symmetry Preserving Surface-State for the Electron Topological Insulator

Chong Wang, Andrew C. Potter, T. Senthil

Strongly Correlated Electrons · Submitted 13 Jun 2013

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

The authors' main claim Here we show that it is possible for the TI surface to be both gapped and symmetry-preserving, at the expense of having surface-topological order.

how it is stated · asserted 0.73 read the record →

Comment (0) Read on arXiv ↗

Cite ▾

arXiv ID1306.3223 (version 3)

Pith IDQ7N5EF3D, Pith's permanent record of this paper and its review

CitationAndrew C. Potter, Chong Wang, T. Senthil. "Gapped Symmetry Preserving Surface-State for the Electron Topological Insulator." arXiv:1306.3223 (2013). https://pith.science/paper/Q7N5EF3D

Claim paper

The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Open the compiled record

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,351 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.09 · states limitation 0.34 · human participants 0.02 · controlled comparison 0.08 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.88 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; show every role.

It is well known that the 3D electronic topological insulator (TI) with charge-conservation and time-reversal symmetry cannot have a trivial insulating surface that preserves symmetry. It is often implicitly assumed that if the TI surface preserves both symmetries then it must be gapless. Here we show that it is possible for the TI surface to be both gapped and symmetry-preserving, at the expense of having surface-topological order. In contrast to analogous bosonic topological insulators, this symmetric surface topological order is intrinsically non-Abelian. We show that the surface-topological order provides a complete non-perturbative definition of the electron TI that transcends a free-particle band-structure picture, and could provide a useful perspective for studying strongly correlated topological Mott insulators.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	It is well known that the 3D electronic topological insulator (TI) with charge-conservation and time-reversal symmetry cannot have a trivial insulating surface that preserves symmetry.	background 1.00	0.03	0.03	asserted 1.00
s1	It is often implicitly assumed that if the TI surface preserves both symmetries then it must be gapless.	background 0.92	0.03	0.03	asserted 0.62
s2	Here we show that it is possible for the TI surface to be both gapped and symmetry-preserving, at the expense of having surface-topological order.	result 0.80	0.94	0.91	asserted 0.73
s3	In contrast to analogous bosonic topological insulators, this symmetric surface topological order is intrinsically non-Abelian.	result 0.97	0.76	0.09	asserted 1.00
s4	We show that the surface-topological order provides a complete non-perturbative definition of the electron TI that transcends a free-particle band-structure picture, and could provide a useful perspective for studying strongly correlated topological Mott insulators.	interpretation 0.96	0.90	0.21	asserted 0.65

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.72.

What was examined, and what was not

sources read

arXiv listing abstract v3

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper

Original abstract

It is well known that the 3D electronic topological insulator (TI) with charge-conservation and time-reversal symmetry cannot have a trivial insulating surface that preserves symmetry. It is often implicitly assumed that if the TI surface preserves both symmetries then it must be gapless. Here we show that it is possible for the TI surface to be both gapped and symmetry-preserving, at the expense of having surface-topological order. In contrast to analogous bosonic topological insulators, this symmetric surface topological order is intrinsically non-Abelian. We show that the surface-topological order provides a complete non-perturbative definition of the electron TI that transcends a free-particle band-structure picture, and could provide a useful perspective for studying strongly correlated topological Mott insulators.

Human review

How Pith checks papers → · Full audit of this paper →

References

Forward citations

Cited by 11 Pith papers

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

Is the Composite Fermion a Dirac Particle?
cond-mat.mes-hall 2015-02 conditional novelty 8.0 of 10

The composite fermion of the half-filled Landau level is a massless Dirac fermion with Berry phase π when particle-hole symmetry is exact.
Classification of interacting electronic topological insulators in three dimensions
cond-mat.str-el 2013-06 conditional novelty 8.0 of 10

Interacting electronic topological insulators in three dimensions fall into exactly eight classes forming a Z_2^3 group, of which six are new and require electron interactions.
Symmetric Gapped Interfaces of SPT and SET States: Systematic Constructions
cond-mat.str-el 2017-05 conditional novelty 7.0 of 10

A finite group extension can trivialize any finite-group SPT cocycle, yielding an exactly soluble symmetry-preserving gapped boundary in any dimension d≥2.
A Duality Web in 2+1 Dimensions and Condensed Matter Physics
hep-th 2016-06 conditional novelty 7.0 of 10

Assuming one boson-fermion duality, the paper derives a connected web of 2+1-dimensional dualities, including a properly quantized fermion-fermion duality, and relates them to 3+1-dimensional S-duality.
Generalized Symmetries of QED$_4$ on Non-Spin Manifolds
hep-th 2026-10 accept novelty 6.0 of 10

On non-spin four-manifolds, QED's magnetic one-form symmetry is 4π-periodic and twisted by the second Stiefel-Whitney class, and rational chiral defects can be completed by neutral Witten-Reshetikhin-Turaev layers.

Show 6 more citing papers

When Symmetries Twist: Anomaly Inflow on Monodromy Defects
hep-th 2026-05 unverdicted novelty 6.0 of 10

Monodromy defects for anomalous symmetries are defined as domain walls between symmetry generators and anomaly-induced topological orders, resulting in protected chiral edge modes and adiabatic pumping of gapless degr...
Chern-Simons-matter dualities with $SO$ and $USp$ gauge groups
cond-mat.str-el 2016-11 accept novelty 6.0 of 10

The authors conjecture SO(N)_k and USp(2N)_k Chern-Simons-matter dualities linking N_f real scalars to N_f real fermions, and pin down the matching pure-Chern-Simons level-rank dualities in a precise spin-TQFT form.
Translational symmetry and microscopic constraints on symmetry-enriched topological phases: a view from the surface
cond-mat.str-el 2015-11 conditional novelty 6.0 of 10

A 2D topological phase whose unit cell carries a projective representation of the symmetry group must have an obstruction class matching that representation, which forces a spinon when the symmetry is continuous or a ...
$S$-duality of $u(1)$ gauge theory with $\theta =\pi$ on non-orientable manifolds: Applications to topological insulators and superconductors
hep-th 2015-10 conditional novelty 6.0 of 10

The gauged class AII topological insulator and the gauged nu=1 class AIII topological superconductor are S-dual at theta equal to pi, verified by matching partition functions on RP4.
Symmetric Mass Generation
cond-mat.str-el 2022-04 accept novelty 3.0 of 10

Symmetric mass generation is a real interaction-driven route to gapping anomaly-free fermions without symmetry breaking, and its known examples can be organized under a parton-based framework.
Zoo of quantum-topological phases of matter
cond-mat.str-el 2016-10 conditional novelty 2.0 of 10

Gapped, featureless quantum liquids at zero temperature can carry two distinct kinds of order, topological order from long-range entanglement and symmetry-protected order from short-range entanglement, and the paper s...

How the literature uses it

24 arXiv papers cite this in 30 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers whose main result relates to this one's

Found among the papers closest to this one by title and main claim. Pith's classifier compared each pair's main results and a second model family confirmed the relation; checked against two further families, shown conflicts agreed 118 times in 120 and shown same results 218 times in 239. The quoted sentence is the other paper's main claim.

States the same result 1 paper

Here we discuss a novel possibility in the presence of interactions, a surface phase that preserves all symmetries but is nevertheless gapped and insulating.

Symmetry Enforced Non-Abelian Topological Order at the Surface of a Topological Insulator · 0.84

Papers citing it · 25 sentences without a confident label

Compares with it 1 paper

Wang et al. [ref] constructing another time-reversal invariant and charge-conserving topological phase, described by the anyon model $.

A Time-Reversal Invariant Topological Phase at the Surface of a 3D Topological Insulator · Conclusion · 0.88

Cites it as background 4 papers

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

Conflicting Symmetries in Topologically Ordered Surface States of Three-dimensional Bosonic Symmetry Protected Topological Phases · Introduction · 0.90
For time-reversal-invariant class AII topological insulators (TI) and class DIII superconductors (TSC), several different approaches, including vortex condensation [ref] , coupled layer constructions [ref] and decorated Walker-Wang models [ref] have been pursued and a number of possible STOs have been identified, leading to a rather complete understanding of the classifications of interacting TIs and TSCs in 3 [ref] .

Microscopic Theory of Surface Topological Order for Topological Crystalline Superconductors · Introduction · 0.94
[ref] A topological order is characterized by a set of anyon types and their topological properties, such as fusion and braiding.

Bulk characterization of topological crystalline insulators: stability under interactions and relations to symmetry enriched U(1) quantum spin liquids · A symmetric surface topological order · 0.93

What it cites · 8 sentences without a confident label

Compares with 3 papers

Qi [ref] which obtains the same STO as in Ref. [ref] .

A Time-Reversal Invariant Topological Phase at the Surface of a 3D Topological Insulator · Discussion · 0.86
Qi [ref] which obtains the same STO as in Ref. [ref] .

Symmetry Enforced Non-Abelian Topological Order at the Surface of a Topological Insulator · Discussion · 0.86
Fisher which obtains the same STO [ref] , and a related work by P.

A symmetry-respecting topologically-ordered surface phase of 3d electron topological insulators · Discussion · 0.86

Cites as background 1 paper

For boson TIs, the lens of STO provides a useful perspective into 3+1D strongly correlated boson TIs as well as 2+1D gauge theories [ref] .

Boson topological insulators: A window into highly entangled quantum phases · Discussion · 0.81

Discussion

Know something about this paper? Leave a comment, or highlight any passage above to comment on it.