We develop a new adiabatic theorem for unique gapped ground states which does not require the gap for local Hamiltonians. We instead require a gap in the bulk and a smoothness of expectation values of sub-exponentially localized observables in the unique gapped ground state $\varphi_s(A)$. This requirement is weaker than the requirement of the gap of the local Hamiltonians, since a uniform spectral gap for finite dimensional ground states implies a gap in the bulk for unique gapped ground states, as well as the smoothness.

中文翻译：

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体中间隙相内的自守等价

我们为独特的有间隙基态开发了一个新的绝热定理，它不需要局部哈密顿量的间隙。相反，我们需要在独特的有间隙的基态 $\varphi_s(A)$ 中，体积中的间隙和次指数局部可观测值的期望值的平滑性。这个要求比局部哈密顿量的间隙要求弱，因为有限维基态的均匀谱间隙意味着独特的有间隙基态的体积间隙以及平滑度。