Connecting the Many-Body Chern Number to Luttinger's Theorem through Středa's Formula

Abstract

Relating the quantized Hall response of correlated insulators to many-body topological invariants is a key challenge in topological quantum matter. Here, we use Streda's formula to derive an expression for the many-body Chern number in terms of the single-particle interacting Green's function and its derivative with respect to a magnetic field. In this approach, we find that this many-body topological invariant can be decomposed in terms of two contributions, $N_3[G]+\Delta N_3[G]$, where $N_3[G]$ is known as the Ishikawa-Matsuyama invariant and where the second term involves derivatives of Green's function and the self energy with respect to the magnetic perturbation. As a by-product, the invariant $N_3[G]$ is shown to stem from the derivative of Luttinger's theorem with respect to the probe magnetic field. These results reveal under which conditions the quantized Hall conductivity of correlated topological insulators is solely dictated by the invariant $N_3[G]$, providing new insight on the origin of fractionalization in strongly-correlated topological phases.

6 pages

References in corpus (14)

• Signatures of Fractional Quantum Anomalous Hall States in Twisted MoTe2 Bilayer
• Integer and fractional Chern insulators in twisted bilayer MoTe2
• Simplified topological invariants for interacting insulators
• Correlation effects in two-dimensional topological insulators
• Realization of a fractional quantum Hall state with ultracold atoms
• Absence of Luttinger's Theorem due to Zeros in the Single-Particle Green Function
• Breakdown of Luttinger's theorem in two-orbital Mott insulators
• Theory of Non-Equilibirum States Driven by Constant Electromagnetic Fields: Non-Commutative Quantum Mechanics in the Keldysh Formalism
• Fractional Chern insulators of few bosons in a box: Hall plateaus from center-of-mass drifts and density profiles
• Failure of Topological Invariants in Strongly Correlated Matter
• Topological interpretation of Luttinger theorem
• Unified role of Green's function poles and zeros in topological insulators
• Hall Coefficient in an Interacting Electron Gas
• Iron phthalocyanine on Au(111) is a "non-Landau" Fermi liquid

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