Quantum Monte Carlo simulation of topological phase transitions

We study the electron-electron interaction effects on topological phase transitions by the ab initio quantum Monte Carlo simulation. We analyze two-dimensional class A topological insulators and three-dimensional Weyl semimetals with the long-range Coulomb interaction. The direct computation of the Chern number shows the electron-electron interaction modifies or extinguishes topological phase transitions.

Figure 1

The Chern number $\langle N\rangle$. The black circles are the numerical solutions and the black dashed line is the analytical solution of the noninteracting case. The colored symbols are quantum Monte Carlo simulation results.

Figure 2

The Berry curvature $F\left(p\right)$ in the noninteracting case. The momentum space $(p_1,p_2)$ is periodic.

Figure 3

The configuration numbers of the Chern number $N$ in the Monte Carlo ensemble with $m/t=1.2$.

Figure 4

Schematic figure of Weyl points (red circles). The Chern number is calculated in the $(p_1,p_2)$ plane with $p_3$ fixed (green sheet).

Figure 5

The Chern number $\langle N\rangle$. The black circles are the numerical solutions and the dashed line is the analytical solution of the noninteracting case. The colored symbols are the quantum Monte Carlo simulation results.

Figure 6

Phase diagram. The Chern number $\langle N\rangle$ at $p_3=0$ is plotted as a topological order parameter. The dashed curve is a hyperbolic tangent function with $e_c\sim 0.21$.