Figure 3
Ground-state energy density.
(a) The ground-state energy density on the lattice scale 
as a function of β. (b) The first-order derivative of the ground-state energy density on the lattice scale 
with respect to β. (c) The second-order derivative of the ground-state energy density on the lattice scale 
with respect to β. It shows a cusp when β = π/3, 2π/3. (d) The third-order derivative of 
with respect to β. It shows discontinuity when β = π/3, 2π/3, so the system undergoes a third order topological quantum phase transition.
