Correlated Fragile Topology: a Parton Approach

Chong Wang; Katherine Latimer

RECORD

Correlated Fragile Topology: a Parton Approach

Katherine Latimer, Chong Wang

Strongly Correlated Electrons · Submitted 30 Jul 2020

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

The authors' main claim In this work we propose a rather general parton construction for such correlation-enabled FTIs.

how it is stated · asserted 0.86 read the record →

Comment (0) Read on arXiv ↗

Cite ▾

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-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 6,264 input tokens.

What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.16 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.61 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

A fragile topological insulator (FTI) can be viewed as an almost-atomic insulator, with emergent negative charges localized at certain real space points, even though the underlying lattice Hilbert space contains only positively charged states. Fragile topology in free fermion systems has been fruitfully studied using modern topological band theory. However, the concept is well defined even for strongly correlated systems, and fragile states that cannot be realized within free fermion band theory exist abundantly. In this work we propose a rather general parton construction for such correlation-enabled FTIs. In our parton construction the associated gauge symmetries are completely Higgsed, resulting in only short-range entangled states. The effective negative charges in the FTIs emerge naturally as the remnants of negatively charged partons. For spinful electrons with $SU(2)$ spin-rotation symmetry, the fragile phases can be viewed as FTIs of charge-$2$, spin singlet bosonic Cooper pairs. We discuss a few examples of correlated FTIs for both spinless and spinful fermions, including some "featureless Mott insulators" on the honeycomb lattice previously discussed in the literature.

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	A fragile topological insulator (FTI) can be viewed as an almost-atomic insulator, with emergent negative charges localized at certain real space points, even though the underlying lattice Hilbert space contains only positively charged states.	background 0.99	0.13	0.07	asserted 0.95
s1	Fragile topology in free fermion systems has been fruitfully studied using modern topological band theory.	background 1.00	0.04	0.02	asserted 0.99
s2	However, the concept is well defined even for strongly correlated systems, and fragile states that cannot be realized within free fermion band theory exist abundantly.	background 0.80	0.09	0.07	asserted 1.00
s3	In this work we propose a rather general parton construction for such correlation-enabled FTIs.	contribution 0.99	0.88	0.18	asserted 0.86
s4	In our parton construction the associated gauge symmetries are completely Higgsed, resulting in only short-range entangled states.	result 0.51	0.87	0.15	asserted 1.00
s5	The effective negative charges in the FTIs emerge naturally as the remnants of negatively charged partons.	interpretation 0.80	0.78	0.21	asserted 1.00
s6	For spinful electrons with $SU(2)$ spin-rotation symmetry, the fragile phases can be viewed as FTIs of charge-$2$, spin singlet bosonic Cooper pairs.	interpretation 0.80	0.65	0.12	asserted 0.68
s7	We discuss a few examples of correlated FTIs for both spinless and spinful fermions, including some "featureless Mott insulators" on the honeycomb lattice previously discussed in the literature.	contribution 0.97	0.68	0.08	asserted 0.96

What kind of paper the classifier reports this is: method or tool 0.67 · evidence from argument 0.54.

What was examined, and what was not

sources read

arXiv listing abstract v2

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

A fragile topological insulator (FTI) can be viewed as an almost-atomic insulator, with emergent negative charges localized at certain real space points, even though the underlying lattice Hilbert space contains only positively charged states. Fragile topology in free fermion systems has been fruitfully studied using modern topological band theory. However, the concept is well defined even for strongly correlated systems, and fragile states that cannot be realized within free fermion band theory exist abundantly. In this work we propose a rather general parton construction for such correlation-enabled FTIs. In our parton construction the associated gauge symmetries are completely Higgsed, resulting in only short-range entangled states. The effective negative charges in the FTIs emerge naturally as the remnants of negatively charged partons. For spinful electrons with $SU(2)$ spin-rotation symmetry, the fragile phases can be viewed as FTIs of charge-$2$, spin singlet bosonic Cooper pairs. We discuss a few examples of correlated FTIs for both spinless and spinful fermions, including some "featureless Mott insulators" on the honeycomb lattice previously discussed in the literature.

Human review

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

How the literature uses it

6 arXiv papers cite this in 7 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 citing it · 2 sentences without a confident label

Compares with it 1 paper

This is analogous to the physics of obstructed insulators, fragile topology and generalized LSM constraints studied in the context of symmetric states [ref] , because in all these cases certain many-body entanglement pattern is incompatible with the properties of local DOF.

Entanglement-enabled symmetry-breaking orders · Introduction · 0.82

Cites it as support 3 papers

The “if" part is hypothetical, but there is no known counterexample to it and it is supported by multiple nontrivial examples [ref] .

Classification of symmetry-enriched topological quantum spin liquids · Framework of classification · 1.00
Indeed, this configuration is where the DOF are on a honeycomb lattice, and it is known that sym-SRE ground states are allowed in this case [ref] , consistent with the absence of any LSM constraint.

Topological characterization of Lieb-Schultz-Mattis constraints and applications to symmetry-enriched quantum criticality · $G_s=p6m$ · 0.97
Indeed, trivial states have been theoretically constructed in various such systems [ref] .

Stiefel Liquids: Possible Non-Lagrangian Quantum Criticality from Intertwined Orders · Anomaly matching · 0.99

Cites it as background 1 paper

Fragile topology is a property of a set of “Wannier-obstructed” gapped electronic bands whose Wannier obstruction can be resolved by adding select trivial bands [ref] .

Fragile topology in line-graph lattices with two, three, or four gapped flat bands · Introduction · 0.99

What it cites · 18 sentences without a confident label

Uses the method or tool of 3 papers

This can be shown using the tool of symmetry indicators (also known as topological quantum chemistry) [ref] .

Topological quantum chemistry · An example on honeycomb lattice · 0.98
This can be shown using the tool of symmetry indicators (also known as topological quantum chemistry) [ref] .

Symmetry-based Indicators of Band Topology in the 230 Space Groups · An example on honeycomb lattice · 0.98
This can be shown using the tool of symmetry indicators (also known as topological quantum chemistry) [ref] .

Wilson loop approach to fragile topology of split elementary band representations and topological crystalline insulators with time reversal symmetry · An example on honeycomb lattice · 0.98

Compares with 1 paper

To make our discussion self-contained, we briefly review the symmetry indicator argument in Appendix [ref].[This makes our FTI more intrinsically correlated than the simplest “featureless Mott insulator" [ref] , which has one positive charge at each hexagon plaquette center and no negative charge (and is therefore not fragile).

Featureless and non-fractionalized Mott insulators on the honeycomb lattice at 1/2 site filling · An example on honeycomb lattice · 0.92

Cites as support 2 papers

Interestingly, there are strongly correlated FTIs that cannot be realized within free fermion band theory, as first demonstrated also in Ref. [ref] .

Fragile topological phases in interacting systems · Introduction · 0.96
A consequence of this definition is that many phases that are fragile within free fermion theory become non-fragile once strong interactions are introduced [ref] .

Shift insulators: rotation-protected two-dimensional topological crystalline insulators · Basic Notions · 0.97

Cites as background 2 papers

These make the systematic theory of FTI in band theory rather complicated (see for example Ref. [ref] ).

Fragile Phases As Affine Monoids: Classification and Material Examples · Summary · 0.81
An elegant illustration of such interplay comes from the study of symmetry-protected topological (SPT) phases of matter [ref] .

Symmetry protected topological orders and the group cohomology of their symmetry group · Introduction · 0.99

Discussion

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