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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Online-Zugang: | https://arxiv.org/abs/2404.05867 |
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| _version_ | 1866914744997249024 |
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| author | Kim, Isaac H. Lin, Ting-Chun Ranard, Daniel Shi, Bowen |
| author_facet | Kim, Isaac H. Lin, Ting-Chun Ranard, Daniel Shi, Bowen |
| contents | We show that in two spatial dimensions, when a quantum state has entanglement entropy obeying a strict area law, meaning $S(A)=α|\partial A| - γ$ for constants $α, γ$ independent of lattice region $A$, then it admits a commuting parent Hamiltonian. More generally, we prove that the entanglement bootstrap axioms in 2D imply the existence of a commuting, local parent Hamiltonian with a stable spectral gap. We also extend our proof to states that describe gapped domain walls. Physically, these results imply that the states studied in the entanglement bootstrap program correspond to ground states of some local Hamiltonian, describing a stable phase of matter. Our result also suggests that systems with chiral gapless edge modes cannot obey a strict area law provided they have finite local Hilbert space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_05867 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Strict area law implies commuting parent Hamiltonian Kim, Isaac H. Lin, Ting-Chun Ranard, Daniel Shi, Bowen Quantum Physics Strongly Correlated Electrons We show that in two spatial dimensions, when a quantum state has entanglement entropy obeying a strict area law, meaning $S(A)=α|\partial A| - γ$ for constants $α, γ$ independent of lattice region $A$, then it admits a commuting parent Hamiltonian. More generally, we prove that the entanglement bootstrap axioms in 2D imply the existence of a commuting, local parent Hamiltonian with a stable spectral gap. We also extend our proof to states that describe gapped domain walls. Physically, these results imply that the states studied in the entanglement bootstrap program correspond to ground states of some local Hamiltonian, describing a stable phase of matter. Our result also suggests that systems with chiral gapless edge modes cannot obey a strict area law provided they have finite local Hilbert space. |
| title | Strict area law implies commuting parent Hamiltonian |
| topic | Quantum Physics Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2404.05867 |