Scaling up the transcorrelated density matrix renormalization group

We developed improved techniques for the transcorrelated density matrix renormalization group (DMRG), in which the ground state of the transcorrelated Hamiltonian is represented as a matrix product state (MPS), and demonstrated large-scale calculations of the ground-state energy of the two-dimensional Fermi-Hubbard model. This talk will highlight how we exploited the entanglement structure of the ground states to increase the accuracy of the MPS representation and optimized the non-linear parameter of the Gutzwiller correlator to mitigate the non-variational nature of the transcorrelated method. We examined systems of size up to 12×12 lattice sites and demonstrated significant improvements over standard non-transcorrelated DMRG for equivalent computational effort. Transcorrelation reduced the error of the ground state energy by 2.4× to 14×, with the smallest improvement seen for a small system at half-filling and the largest improvement in a dilute closed-shell system.