Generalized Real-space Chern Number Formula and Entanglement Hamiltonian

Abstract

We generalize a real-space Chern number formula for gapped free fermions to higher orders. Using the generalized formula, we prove recent proposals for extracting thermal and electric Hall conductance from the ground state via the entanglement Hamiltonian in the special case of non-interacting fermions, providing a concrete example of the connection between entanglement and topology in quantum phases of matter.

9 pages + 3 appendices; v2, typo fixed, improve the abstract and introduction

References in corpus (6)

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• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Bipartite entanglement and entropic boundary law in lattice spin systems
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Cited by in corpus (9)

• Extracting topological orders of generalized Pauli stabilizer codes in two dimensions
• Robustness of topological magnons in disordered arrays of skyrmions
• Many-body systems with spurious modular commutators
• Conformal geometry from entanglement
• Free-Fermion Dynamics with Measurements: Topological Classification and Adaptive Preparation of Topological States
• Global and Local Topological Crystalline Markers for Rotation-Symmetric Insulators
• Immersed figure-8 annuli and anyons
• Rényi-like entanglement probe of the chiral central charge
• Geometric additivity of modular commutator for multipartite entanglement