University of Birmingham > Talks@bham > Theoretical Physics Seminars > Efficient simulation of moire materials using the density matrix renormalization group

Efficient simulation of moire materials using the density matrix renormalization group

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Note: **later time than usual**

I will present infinite density-matrix renormalization group (DMRG) studies of an interacting continuum model of twisted bilayer graphene (tBLG) near the magic angle. (arXiv:2009.02354, arxiv:2012.09885). 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. These difficulties are overcome using a newly developed compression procedure (arXiv:1909.0634) 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, I focus first 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. I then discuss the role of strain in bilayer graphene. DMRG studies reveal that adding strain to bilayer graphene drives a phase transition, which may be responsible for inconsistent experimental findings at integer fillings. These 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 in future work.

This talk is part of the Theoretical Physics Seminars series.

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