Biexciton Condensation in Electron-hole Doped Hubbard Bilayers -- A Sign-Problem-Free Quantum Monte Carlo Study

TL;DR

This study uses a sign-problem-free quantum Monte Carlo method to identify a biexcitonic condensate phase in a doped bilayer Hubbard model, revealing new insights into excitonic orders and phase transitions.

Contribution

We developed a determinant quantum Monte Carlo algorithm that avoids the sign problem for equal and opposite doping, enabling the study of excitonic phases in the bilayer Hubbard model.

Findings

Identified a biexcitonic condensate phase at finite doping.

Observed a competing charge density wave state.

Determined the BKT transition temperature from superfluid density.

Abstract

The bilayer Hubbard model with electron-hole doping is an ideal platform to study excitonic orders due to suppressed recombination via spatial separation of electrons and holes. However, suffering from the sign problem, previous quantum Monte Carlo studies could not arrive at an unequivocal conclusion regarding the presence of phases with clear signatures of excitonic condensation in bilayer Hubbard models. Here, we develop a determinant quantum Monte Carlo (DQMC) algorithm for the bilayer Hubbard model that is sign-problem-free for equal and opposite doping in the two layers, and study excitonic order and charge and spin density modulations as a function of chemical potential difference between the two layers, on-site Coulomb repulsion, and inter-layer interaction. In the intermediate coupling regime and in proximity to the SU(4)-symmetric point, we find a biexcitonic condensate phase at finite electron-hole doping, as well as a competing $(\pi,\pi)$ charge density wave (CDW) state. We extract the Berezinskii-Kosterlitz-Thouless (BKT) transition temperature from superfluid density and a finite size scaling analysis of the correlation functions, and explain our results in terms of an effective biexcitonic hardcore boson model.