Numerical Study of the Heisenberg Antiferromagnet on a Hexagonal Lattice with Long-range Interactions, Using Exact Diagonalization and Machine Learning Methods

Motivated by tight-binding hamiltonians that are relevant to the many-body physics of twisted bilayer graphene, we solve numerically the Heisenberg antiferromagnet in supercells of a hexagonal lattice, including further-neighbor interactions which introduce frustration. We use Machine Learning methods, as well as Exact Diagonalization as a benchmark, to obtain the ground state with a variational approach, and examine the spin correlations in different phases as a function of the various interaction parameters. We also demonstrate how larger system sizes can be studied using a method of carefully designed truncation of the Fock space to keep only the most significant basis states and then expanding the basis until convergence is achieved. We finally discuss the extension of this model to Hubbard-type models that include holes, which allows for the hopping of spins, in order to capture the behavior at small doping away from half- filling.