Topological quantum critical points in the extended Bose-Hubbard model

Abstract

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 it reflects the presence of localized edge states protected by a finite charge gap. Finally, we introduce a super-resolution quantum gas microscopy scheme for dipolar dysprosium atoms, which provides a reliable route towards the experimental study of topological quantum critical points.

Quantum phases of dipolar bosons in one-dimensional optical lattices

“…At the transition separating the HI and the CDW (symmetry-broken) phase the neutral gap vanishes, while the charge gap remains finite. This is as in the T = 0 case, where the transition is of Ising type with central charge c = 1/2 [41,[47][48][49] and the quantum critical point is topological [50]. In the CDW phase the density-wave order parameter reaches a finite value, see the upper panel of Fig.…”

Topological pump and bulk-edge-correspondence in an extended Bose-Hubbard model

“…The demonstration of the SPT phases is essential. So far, in the extended Bose Hubbard model (EBHM) [6][7][8], the Haldane insulator (HI) as an analogue of the S = 1 Haldane phase of the quantum spin chain is investigated [9][10][11][12][13][14][15][16][17][18]. Note that such a HI phase can be realized in fermionic gas trapped in a ladder optical lattice system [19].…”

Revealing the topological nature of the bond order wave in a strongly correlated quantum system

“…Characterization of the topological bulk sector .-For one-dimensional interacting systems, the presence of a SPT phase is signalled by a non-vanishing value of a nonlocal string order parameter [45][46][47] that can be measured in ultracold atomic systems with a quantum gas microscope [63][64][65][66]. In particular, the topological nature of SSH-like chains is captured by the long-range order of the following string correlator [69][70][71]:…”