Microsopic Theory of Spin Polarons in Chern Ferromagnets

TL;DR

This paper develops a microscopic theory of spin polarons in Chern ferromagnets, providing explicit wavefunctions and analyzing their stability and properties across different quantum geometries.

Contribution

It introduces a new variational family of spin polaron wavefunctions with efficient evaluation methods, advancing understanding of excitations in Chern ferromagnets.

Findings

Single-spin-flip ansatz achieves over 99% overlap with exact diagonalization.

Multi-spin-flip energies approach skyrmion regimes.

Quantum geometry influences polaron stability and binding energies.

Abstract

We develop a microscopic theory of charged excitations in an SU(2) Chern ferromagnet and obtain closed-form wavefunctions for a hierarchy of charge-$e$ spin polaron states binding an arbitrary number of spin flips. In an ideal Chern-$1$ band with a normal-ordered contact interaction, we show that these polarons are exact eigenstates of the Hamiltonian with the same energy as single-hole excitations. Away from this ideal limit, we promote these states to a variational family by introducing a single size parameter and a geometry-informed single-particle dressing. Our momentum-space wavefunctions admit two equivalent representations: a ratio of Jastrow factors of Weierstrass functions of relative momenta or an antisymmetrized geminal product of particle-hole wavefunctions. The latter enables efficient evaluation of overlaps and expectation values for large system sizes and many spin flips. Benchmarking in the lowest Landau level, the single-spin-flip ansatz achieves $\gtrsim 99\%$ overlap with exact diagonalization and accurately captures binding energies, while the multi-spin-flip energies interpolate smoothly toward the large-texture (skyrmion) regime. For Chern bands with tunable quantum geometry, we find that interaction-generated single particle dispersion quickly destabilizes the spin polarons once quantum geometry becomes sufficiently non-uniform. When such dispersion is suppressed, however, the bound states persist deeper into the non-uniform regime, with the binding energy slowly decreasing and the bound state becoming larger as the quantum geometry becomes more concentrated. Our results provide a microscopic foundation for analyzing doped Chern ferromagnets in moir\'e platforms and lay the groundwork for variational wavefunctions of multi-polaron excitations and phases.