Disentangled topological numbers by a purification of entangled mixed states for non-interacting fermion systems

Abstract

We argue that the entanglement Chern number proposed recently is invariant under the adiabatic deformation of a gapped many-body groundstate into a {\it disentangled/purified} one, which implies a partition of the Chern number into subsystems (disentangled Chern number). We generalize the idea to another topological number, the Z${}_2$ Berry phase for a system with particle-hole symmetry, and apply it to a groundstate in a weak topological phase where the Chern number vanishes but the groundstate nevertheless has edge states. This entanglement Berry phase is especially useful for characterizing random systems with nontrivial edge states.

6 pages, 3 figures, final version. Open access article in JPSJ

References in corpus (11)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Topological Field Theory of Time-Reversal Invariant Insulators
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Quantum Spin Hall Effect and Topologically Invariant Chern Numbers
• Entanglement Spectrum of a Disordered Topological Chern Insulator
• Topological aspects of quantum spin Hall effect in graphene: Z${}_2$ topological order and spin Chern number
• Bimodal conductance distribution of Kitaev edge modes in topological superconductors
• Entanglement Spectra of the quantum hard-square model: Holographic minimal models
• Entanglement Chern number for an extensive partition of a topological ground state
• Characterizing the weak topological properties: Berry phase point of view
• Tensor Network Implementation of Bulk Entanglement Spectrum

Cited by in corpus (4)

• Disorder Effects in Topological States -- Brief Review of the Recent Developments
• Realizing a symmetry protected topological phase through dimerized interactions
• Entanglement Chern number for three-dimensional topological insulators: Characterization by Weyl points of entanglement Hamiltonians
• Refined Characterization of Lattice Chern Insulators by Bulk Entanglement Spectrum