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BIMSA TQFT and Higher Symmetries Seminar
Entanglement area law and Lieb-Schultz-Mattis theorem in long-range interacting systems, and symmetry-enforced long-range entanglement
Entanglement area law and Lieb-Schultz-Mattis theorem in long-range interacting systems, and symmetry-enforced long-range entanglement
演讲者
Ruizhi Liu
时间
2024年12月17日 09:40 至 11:20
地点
A3-3-301
线上
Zoom 468 248 1222
(BIMSA)
摘要
We leverage a recently discovered connection between the entanglement area law, anomalous symmetries, and Lieb-Schultz-Mattis (LSM) type constraints to analyze certain long-range interacting systems. For two-body interactions, the decay condition requires that the interaction strength decreases faster than r^{-2} where r is the distance between the two spins. In this talk, I will present several fundamental results for this class of long-range interacting systems: (a) Area Law: The gapped ground states of these systems satisfy the area law for entanglement entropy, even in the presence of ground state degeneracy.
(b) LSM Constraints: When anomalous symmetries (discrete or continuous, including lattice translations) are present, such long-range interacting systems cannot support a symmetric gapped ground state.
(c) Symmetry-Enforced Long-Range Entanglement: Pure states symmetric under anomalous symmetries must exhibit long-range entanglement, even if they are not the gapped ground states of any natural Hamiltonian.