From hidden order to skyrmions: Quantum Hall states in an extended Hofstadter-Fermi-Hubbard model

• URL: http://arxiv.org/abs/2509.12184v1
• Date: Mon, 15 Sep 2025 17:45:50 GMT
• Title: From hidden order to skyrmions: Quantum Hall states in an extended Hofstadter-Fermi-Hubbard model
• Authors: Fabian J. Pauw, Ulrich Schollwöck, Nathan Goldman, Sebastian Paeckel, Felix A. Palm,
• Abstract summary: We show the emergence of a spin-polarized $frac13$-Laughlin-like fractional Chern insulators (FCIs)<n>In particular, we find that nearest-neighbor repulsion is sufficient to stabilize both particle- and hole-skyrmions in the ground state around $nu=1$.<n>Our results open new pathways for experimental exploration of FCIs with spin textures in both ultracold atom and electronic systems.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The interplay between topology and strong interactions gives rise to a variety of exotic quantum phases, including fractional quantum Hall (FQH) states and their lattice analogs - fractional Chern insulators (FCIs). Such topologically ordered states host fractionalized excitations, which for spinful systems are often accompanied by ferromagnetism and skyrmions. Here, we study a Hofstadter-Hubbard model of spinful fermions on a square lattice, extended by nearest-neighbor interactions. Using large-scale density matrix renormalization group (DMRG) simulations, we demonstrate the emergence of a spin-polarized $\frac{1}{3}$-Laughlin-like FCI phase, characterized by a quantized many-body Chern number, a finite charge gap, and hidden off-diagonal long-range order. We further investigate the quantum Hall ferromagnet at $\nu=1$ and its skyrmionic excitations upon doping. In particular, we find that nearest-neighbor repulsion is sufficient to stabilize both particle- and hole-skyrmions in the ground state around $\nu=1$, whereas we do not find such textures around $\nu=\frac{1}{3}$. The diagnostic toolbox presented in this work, based on local densities, correlation functions, and spin-resolved observables, is directly applicable in quantum gas microscopy experiments. Our results open new pathways for experimental exploration of FCIs with spin textures in both ultracold atom and electronic systems.

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