Efficient simulation of moiré materials using the density matrix renormalization group

Abstract

Despite considerable interest, it has been difficult to conclusively determine the ground state of twisted bilayer graphene (tBLG), due to the long-range nature of the Coulomb interaction and the fragile topology of the tBLG flat bands. This paper puts forward a method for studying tBLG more efficiently: mixed-$x\phantom{\rule{0}{0ex}}k$ space density-matrix renormalization group (DMRG) with matrix product operator (MPO) compression. The method enables the authors to calculate accurately the ground state of single-valley single-spin tBLG, and it puts DMRG with more degrees of freedom, such as valley, within reach.