Strongly correlated analogues of topological insulators have been explored in
systems with purely on-site symmetries, such as time-reversal or charge
conservation. Here, we use recently developed tensor network tools to study a
quantum state of interacting bosons which is featureless in the bulk, but
distinguished from an atomic insulator in that it exhibits entanglement which
is protected by its spatial symmetries. These properties are encoded in a model
many-body wavefunction that describes a fully symmetric insulator of bosons on
the honeycomb lattice at half filling per site. While the resulting integer
unit cell filling allows the state to bypass `no-go' theorems that trigger
fractionalization at fractional filling, it nevertheless has nontrivial
entanglement, protected by symmetry. We demonstrate this by computing the
boundary entanglement spectra, finding a gapless entanglement edge described by
a conformal field theory as well as degeneracies protected by the non-trivial
action of combined charge-conservation and spatial symmetries on the edge.
Here, the tight-binding representation of the space group symmetries plays a
particular role in allowing certain entanglement cuts that are not allowed on
other lattices of the same symmetry, suggesting that the lattice representation
can serve as an additional symmetry ingredient in protecting an interacting
topological phase. Our results extend to a related insulating state of
electrons, with short-ranged entanglement and no band insulator analogue.Comment: 18 pages, 13 figures Added additional reference