Interaction Enabled Topological Crystalline Phases

Abstract

In this article we provide a general mechanism for generating interaction-enabled fermionic topological phases. We illustrate the mechanism with crystalline symmetry-protected topological phases in 1D and 2D. These non-trivial phases require interactions for their existence and, in the cases we consider, the free-fermion classification yields only a trivial phase. Similar to the interpretation of the Kitaev Majorana wire as a mean-field p-wave superconductor Hamiltonian arising from an interacting model with quartic interactions, we show that our systems can be interpreted as "mean-field" charge-$4e$ superconductors arising, e.g., from an interacting model with eight-body interactions, or through another physical mechanism. The quartet superconducting nature allows for the teleportation of full Cooper pairs, and in 2D for interesting semiclassical crystalline defects with non-Abelian anyon boundstates.

7 pages, 2 figures

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• Building crystalline topological phases from lower-dimensional states
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• Many-body localization in a non-Hermitian quasi-periodic system
• Higher order symmetry-protected topological states for interacting bosons and fermions
• Crystalline topological phases as defect networks
• Real-space recipes for general topological crystalline states
• Interacting Majorana Fermions
• Interaction-induced Liouvillian skin effect in a fermionic chain with a two-body loss
• Interacting Topological Quantum Chemistry in 2D: Many-body Real Space Invariants
• From Dirac semimetals to topological phases in three dimensions: a coupled wire construction
• Reduction of topological $\mathbb{Z}$ classification in cold atomic systems
• Topological Crystalline Magnets: Symmetry-Protected Topological Phases of Fermions
• Surface field theories of point group symmetry protected topological phases
• Synthetic Mechanical Lattices with Synthetic Interactions
• Entanglement Chern number for three-dimensional topological insulators: Characterization by Weyl points of entanglement Hamiltonians
• A search for correlation-induced adiabatic paths between distinct topological insulators
• Quantum Restored Symmetry Protected Topological Phases
• Emergence of non-trivial phases in interacting non-Hermitian quasiperiodic chains with power-law hopping