Geometric approach to fragile topological phases

Topological phases of matter are defined by their nontrivial patterns of ground-state quantum entanglement, which is irremovable so long as the excitation gap and the protecting symmetries, if any, are maintained. Recent studies on noninteracting electrons in crystals have unveiled a peculiar variety of topological phases, which harbor nontrivial entanglement that can be dissolved simply by the the addition of entanglement-free, but charged, degrees of freedom. Such topological phases have a weaker sense of robustness than their conventional counterparts, and are therefore dubbed ``fragile topological phases.'' In this work, we show that fragile topology is a general concept prevailing beyond systems of noninteracting electrons. Fragile topological phases can generally occur when a system has a $\mathrm{U}(1)$ charge conservation symmetry, such that only particles with one sign of the charge are physically allowed (e.g., electrons but not positrons). We demonstrate that fragile topological phases exist in interacting systems of both fermions and of bosons.Topological phases of matter are defined by their nontrivial patterns of ground-state quantum entanglement, which is irremovable so long as the excitation gap and the protecting symmetries, if any, are maintained. Recent studies on noninteracting electrons in crystals have unveiled a peculiar variety of topological phases, which harbor nontrivial entanglement that can be dissolved simply by the the addition of entanglement-free, but charged, degrees of freedom. Such topological phases have a weaker sense of robustness than their conventional counterparts, and are therefore dubbed ``fragile topological phases.'' In this work, we show that fragile topology is a general concept prevailing beyond systems of noninteracting electrons. Fragile topological phases can generally occur when a system has a $\mathrm{U}(1)$ charge conservation symmetry, such that only particles with one sign of the charge are physically allowed (e.g., electrons but not positrons). We demonstrate that fragile topological phases exist in interacting systems of both fermions and of bosons.

arXiv:1809.02128Physical review. B./Physical review. BMar 15, 201948 citations

Disconnected elementary band representations, fragile topology, and Wilson loops as topological indices: An example on the triangular lattice

Barry Bradlyn, Zhijun Wang, Jennifer Cano +1 more

Like all topologically nontrivial bands, the recently discovered fragile topological states cannot be described with symmetric localized basis functions. Unlike the well-understood ``stable'' topological phases, fragile ones have a localized description in the presence of additional trivial orbitals. Here, the authors explore the properties of fragile topological bands, focusing on a family of models on a triangular lattice. The authors show how nonabelian Berry phases can be used to diagnose fragile topology. They also explore how fragile topology manifests itself in the entanglement spectrum.Like all topologically nontrivial bands, the recently discovered fragile topological states cannot be described with symmetric localized basis functions. Unlike the well-understood ``stable'' topological phases, fragile ones have a localized description in the presence of additional trivial orbitals. Here, the authors explore the properties of fragile topological bands, focusing on a family of models on a triangular lattice. The authors show how nonabelian Berry phases can be used to diagnose fragile topology. They also explore how fragile topology manifests itself in the entanglement spectrum.

arXiv:1807.09729Physical review. B./Physical review. BJan 25, 2019142 citations

Space–time geometry of topological phases

F.J. Burnell, Steven H. Simon

arXiv:1004.5586Annals of PhysicsJun 20, 201062 citations

Topological phases in one dimension

Antônio Sérgio Teixeira Pires

Institute of Physics eBooksNov 1, 20210 citations

\mathrm{U}(1)

charge conservation symmetry, such that only particles with one sign of the charge are physically allowed (e.g., electrons but not positrons). We demonstrate that fragile topological phases exist in interacting systems of both fermions and of bosons.