Ground state phase diagram of the half-filled bilayer Hubbard model

TL;DR

This study combines functional renormalization group and quantum Monte Carlo methods to map the ground state phase diagram of the half-filled bilayer Hubbard model, revealing the nature of metallic, Mott-insulating, and band-insulating phases.

Contribution

It provides a comprehensive and unbiased analysis of the phase diagram, clarifying the stability of antiferromagnetic Mott insulators and the transition to band insulators in the model.

Findings

Antiferromagnetic Mott insulator is the dominant instability at weak coupling.

Finite-size effects relate to the two-sheeted Fermi surface structure.

Quantum Monte Carlo effectively identifies the Mott to band insulator transition.

Abstract

Employing a combination of functional renormalization group calculations and projective determinantal quantum Monte Carlo simulations, we examine the Hubbard model on the square lattice bilayer at half filling. From this combined analysis, we obtain a comprehensive account on the ground state phase diagram with respect to the extent of the system's metallic and (antiferromagnetically ordered) Mott-insulating as well as band-insulating regions. By means of an unbiased functional renormalization group approach, we exhibit the antiferromagnetic Mott-insulating state as the relevant instability of the free metallic state, induced by any weak finite onsite repulsion. Upon performing a careful analysis of the quantum Monte Carlo data, we resolve the difficulty of identifying this antiferromagnetic ground state for finite interlayer hopping in the weak-coupling regime, where nonmonotonous finite-size corrections are shown to relate to the two-sheeted Fermi surface structure of the metallic phase. On the other hand, quantum Monte Carlo simulations are well suited to identify the transition between the Mott-insulating phase and the band insulator in the intermediate-to-strong coupling regime. Here, we compare our numerical findings to indications for the transition region obtained from the functional renormalization group procedure.