Detection of Chern numbers and entanglement in topological two-species systems through subsystem winding numbers

Abstract

Topological invariants, such as the Chern number, characterise topological phases of matter. Here we provide a method to detect Chern numbers in systems with two distinct species of fermion, such as spins, orbitals or several atomic states. We analytically show that the Chern number can be decomposed as a sum of component specific winding numbers, which are themselves physically observable. We apply this method to two systems, the quantum spin Hall insulator and a staggered topological superconductor, and show that (spin) Chern numbers are accurately reproduced. The measurements required for constructing the component winding numbers also enable one to probe the entanglement spectrum with respect to component partitions. Our method is particularly suited to experiments with cold atoms in optical lattices where time-of-flight images can give direct access to the relevant observables.

14 pages, 4 figures

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• Time-reversal invariant topological superfluids in Bose-Fermi mixtures
• Diagnosing Topological Edge States via Entanglement Monogamy
• Interaction-Driven Topological Insulator in Fermionic Cold Atoms on an Optical Lattice: A Design with a Density Functional Formalism
• Induced topological order at the boundary of 3D topological superconductors
• Winding number order in the Haldane model with interactions
• Conformal energy currents on the edge of a topological superconductor
• Characterization of helical states in semiconductor quantum wells using quantum information quantities
• Josephson junction arrays as a platform for topological phases of matter
• Interferometric detection of Chern numbers in topological optical lattices