Reduction of topological $\mathbb{Z}$ classification in cold atomic systems

Abstract

One of the most challenging problems in correlated topological systems is a realization of the reduction of topological classification, but very few experimental platforms have been proposed so far. We here demonstrate that ultracold dipolar fermions (e.g., ${}^{167}$Er, ${}^{161}$Dy, and ${}^{53}$Cr) loaded in an optical lattice of two-leg ladder geometry can be the first promising testbed for the reduction $\mathbb{Z}\to {\mathbb{Z}}_4$, where solid evidence for the reduction is available thanks to their high controllability. We further give a detailed account of how to experimentally access this phenomenon; around the edges, the destruction of one-particle gapless excitations can be observed by the local radio frequency spectroscopy, while that of gapless spin excitations can be observed by a time-dependent spin expectation value of a superposed state of the ground state and the first excited state. We clarify that even when the reduction occurs, a gapless edge mode is recovered around a dislocation, which can be another piece of evidence for the reduction.

11 pages, 6 figures

References in corpus (13)

• The density-matrix renormalization group in the age of matrix product states
• Classification of topological insulators and superconductors in three spatial dimensions
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Quantum degenerate dipolar Fermi gas
• A lattice of double wells for manipulating pairs of cold atoms
• Many-body Landau-Zener dynamics in coupled 1D Bose liquids
• Symmetry Protected Topological States of Interacting Fermions and Bosons
• Characterization of a topological Mott insulator in one dimension
• Unconditional quantum-noise suppression via measurement-based quantum feedback
• Quantum phases of bosons in double-well optical lattices
• A chromium dipolar Fermi sea
• CPT theorem and classification of topological insulators and superconductors
• Reduction of $\mathbb{Z}$ classification of a two-dimensional weak topological insulator - real-space DMFT study -

Cited by in corpus (14)

• Interacting topological insulators: a review
• Non-Hermitian perspective of the band structure in heavy-fermion systems
• Exceptional rings in two-dimensional correlated systems with chiral symmetry
• Non-Hermitian topological Mott insulators in one-dimensional fermionic superlattices
• Higher-order Topological Mott Insulators
• Chiral-symmetry protected exceptional torus in correlated nodal-line semi-metals
• Exceptional band touching for strongly correlated systems in equilibrium
• Topological invariants for the Haldane phase of interacting SSH chains -- a functional RG approach
• Magnetic states in a three-dimensional topological Kondo insulator
• Topological inheritance in half-SSH Hubbard models
• Topological d-wave superconductivity in two dimensions
• Three-body constrained bosons in double-well optical lattice
• Berry curvature inside parity-time-symmetry protected exceptional surface
• Non-Abelian geometry, topology, and dynamics of a nonreciprocal Su-Schrieffer-Heeger ladder