Exciton Condensation in Electron-hole Doped Hubbard Bilayers -- A Sign-problem-free Quantum Monte Carlo Study

A long-sought state of matter, exciton condensation, recently has been realized experimentally in several systems. We develop a sign-problem-free Determinant Quantum Monte Carlo (DQMC) algorithm for bilayer Hubbard model with electron-hole doping, which is an ideal platform to study exciton condensation due to the suppression of electron-hole recombination. In square lattice systems, we demonstrate a tendency for exciton condensation at momentum (π, π), and this excitonic order appears to compete with a charge ordered state in the parameter regime we study. Exciton condensation on hexagonal lattices, presumably more pertinent to systems used in previous experimental realizations, has also been investigated and the results will be shown in comparison with square lattice results.