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Solvable Lattice Hamiltonians with Fractional Hall Conductivity

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arxiv 2107.02817 v3 pith:KYASOHM4 submitted 2021-07-06 cond-mat.str-el

Zhaoyu Han , Jing-Yuan Chen This is my paper · ORCID
classification cond-mat.str-el
keywords hamiltoniansconductivityfractionalhalllatticesolvablecircumventclass
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We construct a class of lattice Hamiltonians that exhibit fractional Hall conductivity. These Hamiltonians, while not being exactly solvable, can be controllably solved in their low energy sectors, through a combination of perturbative and exact techniques. Our construction demonstrates a systematic way to circumvent the Kapustin-Fidkowski no-go theorem and is generalizable.

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  1. $\mathrm{SL}(2,\mathbb{Z})$ Theta Subgroup Structure of Maxwell theory in the Lattice Villain Hamiltonian Formulation

    hep-lat 2026-07 conditional novelty 7.0 of 10

    Lattice Villain Maxwell theory realizes the theta subgroup of SL(2,Z) via Hamiltonian operators S and T2, with charge exchange, the Witten effect, and a non-invertible defect with Tambara-Yamagami fusion.

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