Mott insulator–superfluid phase transition in two-band Bose–Hubbard models with gapless nodal lines

Abstract

Recent studies on ultracold atoms have reported the implementation of laser-assisted tunneling in lattice systems, facilitating the realization of topological phases. Motivated by such advances, we investigate a two-band Bose-Hubbard model with its single-particle energy bands showing gapless nodal lines, which can be realized for ultracold atoms in the cubic optical lattices using laser-assisted tunneling. We analyze the superfluid-Mott insulator (MI) phase transition in this model and obtain a global phase diagram by using the strong-coupling expansion method. The excitation spectra in strong and weak coupling limits inherit the topological properties of singleparticle energy bands to show the structures of nodal lines. The topological invariants, the flat surface states and the critical properties are analyzed theoretically in detail. The excitation spectra in the MI and superfluid phases are measurable in ultracold atom experiments to prove our results.

Topological gapless matters in three-dimensional ultracold atomic gases

“…Furthermore, Weyl fermion quasiparticles were shown to emerge in a 3D system of polar particles in magnetic fields 30 and in a topological density wave phase in cold atomic Rydberg-dressed atomic fermions 24 . Similar to the fermionic excitations, Weyl points and nodal rings were also shown to emerge in Bogoliubov excita-tions of bosonic superfluid and Mott insulator phases when bosonic atoms are loaded into a Weyl semimetal or nodal ring optical lattice [149][150][151] .…”

Bogoliubov excitations in a Bose–Hubbard model on a hyperhoneycomb lattice

“…After direct numerical calculations, for a closed loop encircling the nodal lines, we find the Berry phase P B = π, which indicates that the flat surface states exist. [35] In addition, we apply the GP theory to study the edge modes of SF on the hyperhoneycomb lattice, where the system is finite along the z direction and the momentum k x and k y remain good quantum numbers. For certainty, we show the band structures of surface excitations on the zigzag edge of the SF in Fig.…”