# Efficient simulation of magic angle twisted bilayer graphene using the density matrix renormalization group

### APA

Parker, D. (2020). Efficient simulation of magic angle twisted bilayer graphene using the density matrix renormalization group. Perimeter Institute. https://pirsa.org/20100028

### MLA

Parker, Daniel. Efficient simulation of magic angle twisted bilayer graphene using the density matrix renormalization group. Perimeter Institute, Oct. 13, 2020, https://pirsa.org/20100028

### BibTex

@misc{ pirsa_PIRSA:20100028, doi = {10.48660/20100028}, url = {https://pirsa.org/20100028}, author = {Parker, Daniel}, keywords = {Condensed Matter}, language = {en}, title = {Efficient simulation of magic angle twisted bilayer graphene using the density matrix renormalization group}, publisher = {Perimeter Institute}, year = {2020}, month = {oct}, note = {PIRSA:20100028 see, \url{https://pirsa.org}} }

**Collection**

**Subject**

Twisted bilayer graphene (tBLG) is a host to a variety of electronic phases, most notably superconductivity when doped away from putative correlated insulator phases. In order to understand the nature of those phases, numerical simulations such as Hartree-Fock calculation and density matrix renormalization group (DMRG) techniques are essential.

Due to the long-range Coulomb interaction and its fragile topology, however, tBLG is difficult to study with standard DMRG techniques.

In this work, we present how a recently developed MPO compression algorithm can be used to make the problem tractable, and how 1D Wannier localization can be used to circumvent the fragile topology.

As a test case, we apply this technique to the toy model of spinless/single-valley model of tBLG. We find that the ground state is essentially a k-space Slater determinant, confirming the validity of previous Hartree-Fock calculations. If time permits, I will also present our ongoing effort to apply this technique to spinful/valleyful model for tBLG.