No eigenstate of the critical transverse-field Ising chain satisfies the area law
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866911931177107456 |
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| author | Bocini, Saverio Fagotti, Maurizio |
| author_facet | Bocini, Saverio Fagotti, Maurizio |
| contents | We argue that, in a basis common to all one-site shift invariant conserved charges, there is no eigenstate of a noninteracting local spin-1/2 chain Hamiltonian that satisfies the area law if the ground state has half-integer central charge. That is to say, in those models all (quasi)local one-site shift invariant conserved operators are gapless. From the standpoint of bipartite entanglement properties, we show indeed that there are three distinct one-site shift invariant noninteracting models, two of which are equivalent to the XX model (for one of them the transformation breaks one-site shift invariance) and the other to the critical Ising model. The former class has two locally distinct one-site shift invariant excited states satisfying the area law; the latter two classes have none. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2303_09525 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | No eigenstate of the critical transverse-field Ising chain satisfies the area law Bocini, Saverio Fagotti, Maurizio Statistical Mechanics Strongly Correlated Electrons High Energy Physics - Theory Quantum Physics We argue that, in a basis common to all one-site shift invariant conserved charges, there is no eigenstate of a noninteracting local spin-1/2 chain Hamiltonian that satisfies the area law if the ground state has half-integer central charge. That is to say, in those models all (quasi)local one-site shift invariant conserved operators are gapless. From the standpoint of bipartite entanglement properties, we show indeed that there are three distinct one-site shift invariant noninteracting models, two of which are equivalent to the XX model (for one of them the transformation breaks one-site shift invariance) and the other to the critical Ising model. The former class has two locally distinct one-site shift invariant excited states satisfying the area law; the latter two classes have none. |
| title | No eigenstate of the critical transverse-field Ising chain satisfies the area law |
| topic | Statistical Mechanics Strongly Correlated Electrons High Energy Physics - Theory Quantum Physics |
| url | https://arxiv.org/abs/2303.09525 |