An exponentially local spectral flow for possibly non-self-adjoint perturbations of non-interacting quantum spins, inspired by KAM theory

Abstract

Since its introduction by Hastings in [10], the technique of quasi-adiabatic continuation has become a central tool in the discussion and classification of ground state phases. It connects the ground states of self-adjoint Hamiltonians in the same phase by a unitary quasi-local transformation. This paper takes a step towards extending this result to non- self adjoint perturbations, though, for technical reason, we restrict ourselves here to weak perturbations of non-interacting spins. The extension to non-self adjoint perturbation is important for potential applications to Glauber dynamics (and its quantum analogues). In contrast to the standard quasi-adiabatic transformation, the transformation constructed here is exponentially local. Our scheme is inspired by KAM theory, with frustration-free operators playing the role of integrable Hamiltonians.

25 pages, minor corrections, matches published version

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Cited by in corpus (4)

• LDPC stabilizer codes as gapped quantum phases: stability under graph-local perturbations
• Lie-Schwinger block-diagonalization and gapped quantum chains with unbounded interactions
• Stability of invertible, frustration-free ground states against large perturbations
• Local iterative block-diagonalization of gapped Hamiltonians: a new tool in singular perturbation theory