A bootstrap method using density-matrix positivity and steady-state conditions produces bounds on steady-state expectation values, the critical coupling, and the Liouvillian gap for the quantum contact process.
Bootstrapping the gap in quantum spin systems,
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A hierarchy of SDPs yields lower bounds on spectral gaps of frustration-free Hamiltonians that encompass and improve upon Knabe's bound on 1D spin chains.
Derives lower bound on collective mean free path ℓ = √(τ D) in Drude-Kadanoff-Martin model from Green's function bounds, implying Mott-Ioffe-Regel limit for lattice models.
SDP yields exact ground-state energies and fermion correlators for free-fermion spin chains but only qualitative agreement for general Ising/Potts models and requires input that scales poorly with volume.
Bootstrap method in quantum mechanics has an ambiguity problem for mixed potential and operator types, with three proposed resolutions.