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

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.

arXiv:2608.29333 [quant-ph]

(or arXiv:2608.29333v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2608.29333 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.