Metal-insulator transition in transition metal dichalcogenide heterobilayer: accurate treatment of interaction

TL;DR

This study uses advanced quantum Monte Carlo methods to accurately analyze the metal-insulator transition in transition metal dichalcogenide heterobilayers, revealing new insights beyond previous models.

Contribution

It introduces a combined QMC approach for precise modeling of the moiré Hamiltonian and benchmarks density-functional theory against these results.

Findings

Identifies a metal-insulator transition between paramagnetic and Neel ordered states.

Finds significant differences from Hartree-Fock and exact diagonalization results.

Suggests an optimal hybrid functional for DFT approximations.

Abstract

Transition metal dichalcogenide superlattices provide an exciting new platform for exploring and understanding a variety of phases of matter. The moir\'e continuum Hamiltonian, of two-dimensional jellium in a modulating potential, provides a fundamental model for such systems. Accurate computations with this model are essential for interpreting experimental observations and making predictions for future explorations. In this work, we combine two complementary quantum Monte Carlo (QMC) methods, phaseless auxiliary field quantum Monte Carlo and fixed-phase diffusion Monte Carlo, to study the ground state of this Hamiltonian. We observe a metal-insulator transition between a paramagnetic and a $120^\circ$ N\'eel ordered state as the moir\'e potential depth and the interaction strength are varied. We find significant differences from existing results by Hartree-Fock and exact diagonalization studies. In addition, we benchmark density-functional theory, and suggest an optimal hybrid functional which best approximates our QMC results.