Correlated Fragile Topology: a Parton Approach

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.

arXiv comment13 pages

References in corpus (21)

• Topological quantum chemistry
• Symmetry protected topological orders and the group cohomology of their symmetry group
• Symmetry-based Indicators of Band Topology in the 230 Space Groups
• Lieb-Schultz-Mattis in Higher Dimensions
• Topological classification of crystalline insulators through band structure combinatorics
• Origin of Mott insulating behavior and superconductivity in twisted bilayer graphene
• Fragile Topology and Wannier Obstructions
• Fermionic Symmetry Protected Topological Phases and Cobordisms
• Wilson loop approach to fragile topology of split elementary band representations and topological crystalline insulators with time reversal symmetry
• Topological phases protected by point group symmetry
• Symmetry Protected Topological Phases, Anomalies, and Cobordisms: Beyond Group Cohomology
• Gauging spatial symmetries and the classification of topological crystalline phases
• Topology of Disconnected Elementary Band Representations
• Lattice Homotopy Constraints on Phases of Quantum Magnets
• Shift insulators: rotation-protected two-dimensional topological crystalline insulators
• Fragile Phases As Affine Monoids: Classification and Material Examples
• From spinon band topology to the symmetry quantum numbers of monopoles in Dirac spin liquids
• Fragile topological phases in interacting systems
• Featureless and non-fractionalized Mott insulators on the honeycomb lattice at 1/2 site filling
• Featureless quantum insulator on the honeycomb lattice
• The Existence of Featureless Paramagnets on the Square and the Honeycomb Lattices in 2+1D

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• Interacting second-order topological insulators in one-dimensional fermions with correlated hopping
• Classification of symmetry-enriched topological quantum spin liquids
• Mott transition and magnetism in a fragile topological insulator
• Entanglement-enabled symmetry-breaking orders