[PDF] No eigenstate of the critical transverse-field Ising chain satisfies the area law-论文阅读讨论-ReadPaper

摘要

We argue that, in a basis common to all one-site shift invariant conservedcharges, there is no eigenstate of a noninteracting local spin-1/2 chainHamiltonian that satisfies the area law if the ground state has half-integercentral charge. That is to say, in those models all (quasi)local one-site shiftinvariant conserved operators are gapless. From the standpoint of bipartiteentanglement properties, we show indeed that there are three distinct one-siteshift invariant noninteracting models, two of which are equivalent to the XXmodel (for one of them the transformation breaks one-site shift invariance) andthe other to the critical Ising model. The former class has two locallydistinct one-site shift invariant excited states satisfying the area law; thelatter two classes have none.

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