Real-space topology and charge order in the Haldane-Holstein Model

Abstract

We study the half-filled Haldane-Holstein model, where a paradigmatic Chern insulator is coupled to fully dynamical phonons, and provide an unbiased characterization of how retarded electron-phonon interactions destabilize Chern topology. Using determinant quantum Monte Carlo, we find that increasing the coupling drives an abrupt, first-order transition from a Chern insulator to a staggered charge-density wave that acts as a dynamical sublattice (Semenoff) mass. The transition is simultaneously signaled by a nearly quantized many-body Bott index and a real-space local Chern marker constructed from the interacting Green's function, both of which collapse as the charge order parameter becomes extensive. Spectral and open-boundary calculations reveal concomitant gap closing and the loss of boundary spectral weight at the critical coupling. Despite the generic phase problem induced by broken time-reversal symmetry, we show that it remains mild in the low-frequency regime and that the average phase factor sharply tracks the Chern insulator-charge density wave boundary. Our results establish a concrete route by which electron-phonon coupling can trigger a discontinuous collapse of Chern topology and provide experimentally relevant signatures for correlated topological platforms.

References in corpus (20)

• Correlation effects in two-dimensional topological insulators
• Valence Bond Solids and Their Quantum Melting in Hard-Core Bosons on the Kagome Lattice
• Interaction effects and quantum phase transitions in topological insulators
• Interplay of Fractional Chern Insulator and Charge-Density-Wave Phases in Twisted Bilayer Graphene
• Topological charge density waves at half-integer filling of a moiré superlattice
• Imaging tunable quantum Hall broken-symmetry orders in graphene
• Electron-phonon coupling and the Coexistence of Superconductivity and Charge-Density Wave in Monolayer NbSe2
• Topological Phases in AB-Stacked MoTe${}_2$/WSe${}_2$: ${\mathbb{Z}}_2$ Topological Insulators, Chern Insulators, and Topological Charge Density Waves
• Topological Mott Insulator at Quarter Filling in the Interacting Haldane Model
• Topological phase transition in a generalized Kane-Mele-Hubbard model: A combined Quantum Monte Carlo and Green's function study
• Universal topological marker
• Band Collapse and the Quantum Hall Effect in Graphene
• On the Melting of Bosonic Stripes
• Universality and Critical Exponents of the Fermion Sign Problem
• Topological marker approach to an interacting Su-Schrieffer-Heeger model
• Phase transitions in the Haldane-Hubbard model
• A real-space many-body marker for correlated ${\mathbb{Z}}_2$ topological insulators
• The half-filled extended Hubbard model on a square lattice: Phase boundaries from determinant quantum Monte Carlo simulations
• The extended Hubbard model on a honeycomb lattice
• Interaction-induced phases in the half-filled Bernevig-Hughes-Zhang model in one dimension