PIRSA:20100028

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

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

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 

          @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}}
          }

Daniel Parker Virginia Polytechnic Institute and State University

DOI 10.48660/20100028
Collection
Talk Type Scientific Series
Subject

Abstract

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.