Bulk Entanglement Spectrum in Gapped Spin Ladders

TL;DR

This paper investigates the bulk entanglement spectrum of gapped spin ladder ground states, revealing distinctions between half-integer and integer spins and illustrating that critical entanglement Hamiltonians can occur in trivial states.

Contribution

It characterizes the bulk entanglement Hamiltonian for various spin ladder states, generalizes known models, and shows that critical entanglement spectra are not exclusive to topological phases.

Findings

Half-integer spin ladders have gapless or degenerate entanglement spectra.

Integer spin ladders generally exhibit an entanglement gap.

Critical entanglement Hamiltonians can appear in trivial higher-spin states.

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.