Quantum Monte Carlo simulation of a two-dimensional Majorana lattice model

We study interacting Majorana fermions in two dimensions as a low-energy effective model of a vortex lattice in two-dimensional time-reversal-invariant topological superconductors. For that purpose, we implement ab initio quantum Monte Carlo simulation to the Majorana fermion system in which the path-integral measure is given by a semipositive Pfaffian. We discuss spontaneous breaking of time-reversal symmetry at finite temperatures.

Figure 1

Mean-field results of the pair condensate $\langle i{\psi }_{\uparrow }{\psi }_{\downarrow }\rangle$ as a function of temperature $T$.

Figure 2

Monte Carlo data of the pair condensate $\langle i{\psi }_{\uparrow }{\psi }_{\downarrow }\rangle$ as a function of temperature $T$. The noninteracting value ${\langle i{\psi }_{\uparrow }{\psi }_{\downarrow }\rangle }_0$ is subtracted from the Monte Carlo result $\langle i{\psi }_{\uparrow }{\psi }_{\downarrow }\rangle$.

Figure 3

Phase diagram on the $\left(g,T\right)$ plane. The black solid line is the mean-field result of the phase-transition line. The blue gradation is the Monte Carlo data of the subtracted condensate $\langle i{\psi }_{\uparrow }{\psi }_{\downarrow }\rangle -{\langle i{\psi }_{\uparrow }{\psi }_{\downarrow }\rangle }_0$.