Science Advances

This PDF file includes:

• Section S1. Flux attachment in 2D
• Section S2. Implementing matter coupled to a ℤ₂ gauge field in the two-leg ladder geometry
• Section S3. Gauge structure of two-leg ladders
• Section S4. Phase transitions of gauge and matter fields
• Fig. S1. Renormalized tunneling amplitudes determined by Bessel functions.
• Fig. S2. Two-site two-particle problem.
• Fig. S3. Flux attachment in a 2D Hofstadter model.
• Fig. S4. Derivation of the effective Hamiltonian.
• Fig. S5. Wilson loop scaling.
• Fig. S6. The Green’s function in the charge sector.
• Fig. S7. The Luttinger-K parameter.
• Fig. S8. Rung-Mott state at commensurate filling.
• Fig. S9. Phase diagram of the ℤ₂ LGT on a two-leg ladder for commensurate filling.
• Fig. S10. Transition in the gauge sector.
• References (70–74)

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