4.6 Article

Efficient simulation of moire materials using the density matrix renormalization group

期刊

PHYSICAL REVIEW B
卷 102, 期 20, 页码 -

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AMER PHYSICAL SOC
DOI: 10.1103/PhysRevB.102.205111

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资金

  1. NSF Graduate Research Fellowship Program [NSF DGE 1752814]
  2. Office of Science, Office of Basic Energy Sciences, Materials Sciences and Engineering Division of the US Department of Energy [DE-AC02-05-CH11231, KCWF16]
  3. US Department of Energy, Office of Science, Office of Basic Energy Sciences, Materials Sciences and Engineering Division [DE-AC02-05CH11231]
  4. US Department of Energy, Office of Science, Office of Basic Energy Sciences, Materials Sciences and Engineering Division through the Scientific Discovery through Advanced Computing (SciDAC) program [KC23DAC]

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We present an infinite density-matrix renormalization group (DMRG) study of an interacting continuum model of twisted bilayer graphene (tBLG) near the magic angle. 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. To overcome these difficulties, we use a recently developed compression procedure 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, we focus mainly 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. Our results show that the effects of long-range interactions in magic angle graphene can be efficiently simulated with DMRG and open up a new route for numerically studying strong correlation physics in spinful, two-valley tBLG, and other moire materials in future work.

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