Manuscript Oai265-A@2 · Oai265-A.tex · proposition · c0a34a45

Proposition: A static product record has no forced turnover

Static spatial bounds do not determine temporal histories › A stationary bond-dimension-one example · lines 1483–1500 · proof included or linked

Oai265-A@2#prop:stationary

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For

H_{0} = x \in Λ \sum (I - ∣0 ⟩ ⟨ 0 ∣_{x}), Ω_{0} = x \in Λ ⨂ ∣0 ⟩_{x},

the ground state is unique, the gap is one, all subsystem entropies vanish, and the state is an exact bond-dimension-one PEPS. Its Schrödinger evolution under $H_{0}$ is stationary.

Proof. The on-site commuting projectors have a common one-dimensional kernel and smallest positive eigenvalue one. The vector is a product and has energy zero.

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unlabeled · line 1486
$H_{0} = x \in Λ \sum (I - ∣0 ⟩ ⟨ 0 ∣_{x}), Ω_{0} = x \in Λ ⨂ ∣0 ⟩_{x},$

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section: A stationary bond-dimension-one example