Efficient simulation of moire materials using the density matrix renormalization group

TL;DR

This paper demonstrates an efficient DMRG-based method to simulate the complex long-range interactions in twisted bilayer graphene, revealing a nematic semimetal ground state at half-filling and enabling future studies of correlated moire materials.

Contribution

The authors develop a matrix product operator representation for tBLG Hamiltonian that handles long-range Coulomb interactions and multiple degrees of freedom efficiently, advancing numerical simulation capabilities.

Findings

Ground state at half-filling is a nematic semimetal.

Hartree-Fock and DMRG results are nearly identical for the spinless, single-valley case.

Long-range interactions in tBLG can be effectively simulated with the proposed DMRG approach.

Abstract

We present an infinite density-matrix renormalization group (DMRG) study of an interacting continuum model of twisted bilayer graphene (tBLG) near the magic angle. Because of the long-range Coulomb interaction and the large number of orbital degrees of freedom, tBLG is difficult to study with standard DMRG techniques -- even constructing and storing the Hamiltonian already poses a major challenge. To overcome these difficulties, we use a recently developed compression procedure to obtain a matrix product operator representation of the interacting tBLG Hamiltonian which we show is both efficient and accurate even when including the spin, valley and orbital degrees of freedom. To benchmark our approach, we focus mainly on the spinless, single-valley version of the problem where, at half-filling, we find that the ground state is a nematic semimetal. Remarkably, we find that the ground state is essentially a k-space Slater determinant, so that Hartree-Fock and DMRG give virtually identical results for this problem. Our results show that the effects of long-range interactions in magic angle graphene can be efficiently simulated with DMRG, and opens up a new route for numerically studying strong correlation physics in spinful, two-valley tBLG, and other moire materials, in future work.