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

The interplay between topology and strong interactions gives rise to a variety of exotic quantum phases, including fractional quantum Hall states and their lattice analogs—fractional Chern insulators (FCIs). Such topologically ordered states host fractionalized excitations and, 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 simulations, we demonstrate the emergence of a spin-polarized <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:mstyle scriptlevel="1" displaystyle="false"> <a:mn>1</a:mn> </a:mstyle> <a:mo>/</a:mo> <a:mstyle scriptlevel="1" displaystyle="false"> <a:mn>3</a:mn> </a:mstyle> </a:mrow> </a:math> -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 <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"> <f:mrow> <f:mi>ν</f:mi> <f:mo>=</f:mo> <f:mn>1</f:mn> </f:mrow> </f:math> 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 <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"> <g:mrow> <g:mi>ν</g:mi> <g:mo>=</g:mo> <g:mn>1</g:mn> </g:mrow> </g:math> , whereas we do not find such textures around <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"> <h:mrow> <h:mi>ν</h:mi> <h:mo>=</h:mo> <h:mstyle scriptlevel="1" displaystyle="false"> <h:mn>1</h:mn> </h:mstyle> <h:mo>/</h:mo> <h:mstyle scriptlevel="1" displaystyle="false"> <h:mn>3</h:mn> </h:mstyle> </h:mrow> </h:math> . 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.