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PIRSA:20100028

Video URL

https://pirsa.org/20100028

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

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

Daniel Parker Virginia Polytechnic Institute and State University

Talk numberPIRSA:20100028
DOI10.48660/20100028
Source RepositoryPIRSA
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.