Quantized and maximum entanglement from sublattice symmetry

authored by: Henrik Wilming, Tobias J. Osborne
Abstract: We observe that the many-body eigenstates of any quadratic, fermionic Hamiltonian with sublattice symmetry have quantized entanglement entropies between the sublattices: the entanglement comes in multiple singlets. Moreover, such systems always have a ground state that is maximally entangled between the two sublattices. In fact, we also show that under the same assumptions there always exists a (potentially distinct) basis of energy eigenstates that do not conserve the particle number in which each energy eigenstate is maximally entangled between the sublattices. No additional properties, such as translation invariance, are required. We also show that the quantization of ground-state entanglement may persist when interactions are introduced.
Organisation(s): Institute of Theoretical Physics
QuantumFrontiers
CRC 1227 Designed Quantum States of Matter (DQ-mat)
Type: Article
Journal: Physical Review A
Volume: 107
ISSN: 2469-9926
Publication date: 02.2023
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Atomic and Molecular Physics, and Optics
Electronic version(s): https://doi.org/10.48550/arXiv.2112.15177 (Access: Open)
https://doi.org/10.1103/PhysRevA.107.022418 (Access: Closed)

BibTeX

@article{9fc981d825cf48bca0346fdf3df77685,
title = "Quantized and maximum entanglement from sublattice symmetry",
abstract = "We observe that the many-body eigenstates of any quadratic, fermionic Hamiltonian with sublattice symmetry have quantized entanglement entropies between the sublattices: the entanglement comes in multiple singlets. Moreover, such systems always have a ground state that is maximally entangled between the two sublattices. In fact, we also show that under the same assumptions there always exists a (potentially distinct) basis of energy eigenstates that do not conserve the particle number in which each energy eigenstate is maximally entangled between the sublattices. No additional properties, such as translation invariance, are required. We also show that the quantization of ground-state entanglement may persist when interactions are introduced.",
author = "Henrik Wilming and Osborne, {Tobias J.}",
note = "Funding Information: We thank Z. Zimbor{\'a}s and C. Karrasch for valuable correspondence. Support from the DFG through SFB 1227 (DQ-mat) and Quantum Valley Lower Saxony and funding by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany's Excellence Strategy EXC-2123 QuantumFrontiers 390837967 are also acknowledged. ",
year = "2023",
month = feb,
doi = "10.48550/arXiv.2112.15177",
language = "English",
volume = "107",
journal = "Physical Review A",
issn = "2469-9926",
publisher = "American Physical Society",
number = "2",
}