Quantum mechanics

Theoretical physics

Topological quantum number

Gapless playback

Quantum phases

Hubbard model

Phase transition

Topological degeneracy

Critical point (mathematics)

Mathematical optimization

Hamiltonian (control theory)

Symmetry protected topological order

Physics

Topological order

Mathematics

Superconductivity

Condensed matter physics

Geometry

Quantum

Combinatorics

Topological entropy in physics

Topology (electrical circuits)

Quantum phase transition

Bose–Hubbard model

Critical phenomena

Quantum critical point

Physical Review Letters

The combination of topology and quantum criticality can give rise to an exotic mix of counterintuitive effects. Here, we show that unexpected topological properties take place in a paradigmatic strongly correlated Hamiltonian: the 1D extended Bose-Hubbard model. In particular, we reveal the presence of two distinct topological quantum critical points with localized edge states and gapless bulk excitations. Our results show that the topological critical points separate two phases, one topologically protected and the other topologically trivial, both characterized by a long-range ordered string correlation function. The long-range order persists also at the topological critical points and explains the presence of localized edge states protected by a finite charge gap. Finally, we introduce a superresolution quantum gas microscopy scheme for dipolar dysprosium atoms, which provides a reliable route towards the experimental study of topological quantum critical points.

Topological Quantum Critical Points in the Extended Bose-Hubbard Model