Bulk entanglement spectrum in gapped spin ladders
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. © 2016 American Physical Society.