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arXiv · 2608.29333

Zero-Energy Problems for Supersymmetric Hamiltonians on a Chain Are $\mathrm{QMA}_1$-Complete

Yibin Wang
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Abstract

We study exact zero modes of supersymmetric quantum systems whose interactions are arranged on a one-dimensional chain. For Hermitian supercharges, deciding whether a zero mode exists is $\mathrm{QMA}_1$-complete, and the hard instances are geometrically local on a chain. We also classify an explicitly encoded nilpotent $\mathcal{N}=2$ formulation: its exact-zero problem is $\mathrm{QMA}_1$-complete, including the restriction in which the associated Hamiltonian is local on a chain. Both classifications use a verification theorem for simultaneous sparse linear constraints and the same one-dimensional frustration-free Hamiltonian construction. The construction gives an explicit inverse-polynomial lower bound on the ground energy of every reduced NO instance, separating it from zero.

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Yibin Wang. 2026-08-29. Zero-Energy Problems for Supersymmetric Hamiltonians on a Chain Are $\mathrm{QMA}_1$-Complete. https://arxiv.org/abs/2608.29333

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