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Bulk Entanglement Spectrum in Gapped Spin Ladders
Strongly Correlated Electrons · Submitted 4 Nov 2015
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Finally, we give an example of a series of trivial states of higher spin $S>1$ in which the bulk entanglement Hamiltonian is critical, signaling that the relation between topological states and a critical bulk entanglement Hamiltonian is not unique to topological systems.
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The abstract, sentence by sentence
We study the bulk entanglement of a series of gapped ground states of spin ladders, representative of the Haldane phase. These ground states of spin $S/2$ ladders generalize the valence bond solid ground state. In the case of spin 1/2 ladders, we study a generalization of the Affleck-Kennedy-Lieb-Tasaki and Nersesyan-Tsvelik states and fully characterize the bulk entanglement Hamiltonian. In the case of general spin $S$ we argue that in the Haldane phase the bulk entanglement spectrum of a half integer ladder is either gapless or possess a degenerate ground state. For ladders with integer valued spin particles, the generic bulk entanglement spectrum should have an entanglement gap. Finally, we give an example of a series of trivial states of higher spin $S>1$ in which the bulk entanglement Hamiltonian is critical, signaling that the relation between topological states and a critical bulk entanglement Hamiltonian is not unique to topological systems.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We study the bulk entanglement of a series of gapped ground states of spin ladders, representative of the Haldane phase. | contribution 1.00 | 0.93 | 0.05 | asserted 0.96 |
| s1 | These ground states of spin $S/2$ ladders generalize the valence bond solid ground state. | background 0.83 | 0.26 | 0.04 | asserted 1.00 |
| s2 | In the case of spin 1/2 ladders, we study a generalization of the Affleck-Kennedy-Lieb-Tasaki and Nersesyan-Tsvelik states and fully characterize the bulk entanglement Hamiltonian. | contribution 0.90 | 0.93 | 0.09 | asserted 1.00 |
| s3 | In the case of general spin $S$ we argue that in the Haldane phase the bulk entanglement spectrum of a half integer ladder is either gapless or possess a degenerate ground state. | result 0.94 | 0.72 | 0.43 | hedged possibility 0.65 |
| s4 | For ladders with integer valued spin particles, the generic bulk entanglement spectrum should have an entanglement gap. | result 0.89 | 0.38 | 0.20 | hedged possibility 0.79 |
| s5 | Finally, we give an example of a series of trivial states of higher spin $S>1$ in which the bulk entanglement Hamiltonian is critical, signaling that the relation between topological states and a critical bulk entanglement Hamiltonian is not unique to topological systems. | interpretation 0.48 | 0.91 | 0.14 | asserted 0.88 |
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Original abstract
We study the bulk entanglement of a series of gapped ground states of spin ladders, representative of the Haldane phase. These ground states of spin $S/2$ ladders generalize the valence bond solid ground state. In the case of spin 1/2 ladders, we study a generalization of the Affleck-Kennedy-Lieb-Tasaki and Nersesyan-Tsvelik states and fully characterize the bulk entanglement Hamiltonian. In the case of general spin $S$ we argue that in the Haldane phase the bulk entanglement spectrum of a half integer ladder is either gapless or possess a degenerate ground state. For ladders with integer valued spin particles, the generic bulk entanglement spectrum should have an entanglement gap. Finally, we give an example of a series of trivial states of higher spin $S>1$ in which the bulk entanglement Hamiltonian is critical, signaling that the relation between topological states and a critical bulk entanglement Hamiltonian is not unique to topological systems.
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By using a symmetric bulk bipartition [ref] , we can create an array of fractionalized spin-S/2 edge states with super unit cell $l$ in the reduced bulk system.
Quantum antiferromagnetic Heisenberg half-odd integer spin model as the entanglement Hamiltonian of the integer spin Affleck-Kennedy-Lieb-Tasaki states · Introduction · 0.83
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Cites as background 1 paper
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Examples include momentum-space partitions [ref] , a partition between spin and orbital degrees of freedom [ref] , and an extensive real-space partition which is referred to as the bulk entanglement spectrum (BES) [ref] .
Momentum-Space Entanglement in Heisenberg Spin-Half Ladders · Introduction · 0.92
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