Topological Crystalline Bose Insulator in Two Dimensions via Entanglement Spectrum - eScholarship

F. D. M. Haldane

Ashvin Vishwanath, Yi Zhang, Ari M. Turner

Yuting Hu, Yong-Shi Wu

Hiromu Araki, Takahiro Fukui, Yasuhiro Hatsugai

Brayden Ware, Itamar Kimchi, S. A. Parameswaran +1 more

Strongly correlated analogs 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 wave function 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 nontrivial 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 analog.

Alejandro José Uría-Álvarez, Daniel Molpeceres-Mingo, Juan Jose Palacios

Calculation of topological invariants for crystalline systems is well understood in reciprocal space, allowing for the topological classification of a wide spectrum of materials. In this work, we present a technique based on the entanglement spectrum, which can be used to identify the hidden topology of systems without translational invariance. By training a neural network to distinguish between trivial and topological phases using the entanglement spectrum obtained from crystalline or weakly disordered phases, we can predict the topological phase diagram for generic disordered systems. This approach becomes particularly useful for gapless systems, while providing a computational speed-up compared to the commonly used Wilson loop technique for gapful situations. Our methodology is illustrated in two-dimensional models based on the Wilson-Dirac lattice Hamiltonian.