Many-body Chern number without integration

Abstract

The celebrated work of Niu, Thouless, and Wu demonstrated the quantization of Hall conductance in the presence of many-body interactions by revealing the many-body counterpart of the Chern number. The generalized Chern number is formulated in terms of the twisted angles of the boundary condition, instead of the single particle momentum, and involves an integration over all possible twisted angles. However, this formulation is physically unnatural, since topological invariants directly related to observables should be defined for each Hamiltonian under a fixed boundary condition. In this work, we show via numerical calculations that the integration is indeed unnecessary - the integrand itself is effectively quantized and the error decays exponentially with the system size. This implies that the numerical cost in computing the many-body Chern number could, in principle, be significantly reduced as it suffices to compute the Berry connection for a single value of the twisted boundary condition if the system size is sufficiently large.

References in corpus (22)

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Cited by in corpus (46)

• Relations between topology and the quantum metric for Chern insulators
• Many-body topology of non-Hermitian systems
• Kähler geometry and Chern insulators: Relations between topology and the quantum metric
• Non-Hermitian fractional quantum Hall states
• Detecting fractional Chern insulators through circular dichroism
• Fractional Chern insulators of few bosons in a box: Hall plateaus from center-of-mass drifts and density profiles
• Bounds in Nonequilibrium Quantum Dynamics
• Extraction of many-body Chern number from a single wave function
• Probing localization and quantum geometry by spectroscopy
• Interaction Induced Topological Charge Pump
• A generalized boundary condition applied to Lieb-Schultz-Mattis type ingappabilities and many-body Chern numbers
• Connecting the Many-Body Chern Number to Luttinger's Theorem through Středa's Formula
• Quantum phases and topological properties of interacting fermions in one-dimensional superlattices
• Quantum weight: A fundamental property of quantum many-body systems
• Many-Body Invariants for Chern and Chiral Hinge Insulators
• Quench Dynamics and Hall Response of Interacting Chern Insulators
• Interaction-driven topological phase transitions in fermionic SU($3$) systems
• Experimental demonstration of topological bounds in quantum metrology
• Large-$N$ Chern insulators: lattice field theory and quantum simulation approaches to correlation effects in the quantum anomalous Hall effect
• Topological invariants for interacting systems: from twisted boundary condition to center-of-mass momentum
• Manifestation of topological behaviors in interacting Weyl systems: one-body verse two-body correlations
• Quasiparticles as Detector of Topological Quantum Phase Transitions
• Topological linear response of hyperbolic Chern insulators
• Altermagnetic Instabilities from Quantum Geometry
• A real-space many-body marker for correlated ${\mathbb{Z}}_2$ topological insulators
• Calculations of Chern number: equivalence of real-space and twisted-boundary-condition formulae
• Robust measurement of wave function topology on NISQ quantum computers
• Green's Function Approach to Interacting Higher-order Topological Insulators
• Plateau transitions of spin pump and bulk-edge correspondence
• Quantum computing topological invariants of two-dimensional quantum matter
• Composite anyons on a torus
• Relating the Hall conductivity to the many-body Chern number using Fermi's Golden rule and Kramers-Kronig relations
• Localization anisotropy and complex geometry in two-dimensional insulators
• Topological phase in the extended Haldane-Hubbard model with sublattice-dependent repulsion
• Quantum Transport Theory of Strongly Correlated Matter
• Flow of unitary matrices: Real-space winding numbers in one and three dimensions
• Many-body Chern insulator in the Kondo lattice model on a triangular lattice
• Stability of quasi-particle creation and multiband geometry in fractional Chern insulators under magnetic fields
• Structure of the nearly-degenerate manifold of lattice quasiholes on a torus
• Critical Behavior and Duality in Dimensionally Reduced Planar Chern-Simons Superconductors
• Topological Triviality of Flat Hamiltonians
• Topological Order Without Band Topology in Moiré Graphene
• Crossover from Integer to Fractional Quantum Hall Effect
• Tri-component-pairing chiral superconductivity on the honeycomb lattice with mixed $s$- and $d$-wave symmetries
• Disorder-Induced Topological Phases in a Two-Dimensional Chern Insulator with Strong Magnetic Disorder
• Quantized and nonquantized Hall response in topological Hatsugai-Kohmoto systems