Wilson-Loop-Ideal Bands and General Idealization Article Swipe

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Jiabin Yu , Bong H. Lian , Shinsei Ryu ·

YOU? · · 2025 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2509.05410

Quantum geometry is universally bounded from below by Wilson-loop windings. In this work, we define an isolated set of bands to be Wilson-loop-ideal, if their quantum metric saturates the Wilson-loop lower bound. The definition naturally incorporates the known Chern-ideal and Euler-ideal bands, and allows us to define other types of ideal bands, such as Kane-Mele $Z_2$-ideal bands. In particular, we find that an isolated set of two $Z_2$-ideal bands with non-singular nonabelian Berry curvature always admits a Chern-ideal gauge (i.e., effectively behaving as two decoupled Chern-ideal bands), even in the absence of any global good quantum number (such as spin). This enables the direct construction of fractional topological insulator wavefunctions. We further propose a general framework of constructing monotonic flows that achieve Wilson-loop-ideal states starting from non-ideal bands through band mixing, where Wilson-loop-ideal states are not energy eigenstates but have smooth projectors similar to isolated bands. We apply the constructed flows to the realistic model of $3.89^\circ$ twisted bilayer MoTe$_2$ and a moiré Rashba model, and numerically find Chern-ideal and $Z_2$-ideal states, respectively, with relative error in the integrated quantum metric below $5\times 10^{-3}$. Our general definition of Wilson-loop-ideal bands and general procedure of constructing Wilson-loop-ideal states provide a solid basis for future study of novel correlated physics.

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Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/2509.05410
PDF: https://arxiv.org/pdf/2509.05410
OA Status: green
OpenAlex ID: https://openalex.org/W4415059054

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OpenAlex ID: https://openalex.org/W4415059054

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DOI: https://doi.org/10.48550/arxiv.2509.05410

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Title: Wilson-Loop-Ideal Bands and General Idealization

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Type: preprint

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Language: en

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Publication year: 2025

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Publication date: 2025-09-05

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Authors: Jiabin Yu, Bong H. Lian, Shinsei Ryu

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Landing page: https://arxiv.org/abs/2509.05410

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PDF URL: https://arxiv.org/pdf/2509.05410

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Cited by: 0

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