DMRG-based downfolding of strongly correlated materials

The derivation of low-energy effective Hamiltonians ("downfolding") is crucial in understanding emergent phenomena in quantum materials. In this talk, I will demonstrate how density-matrix renormlaization group (DMRG) simulations can facilitate a controlled downfolding procedure for the cuprates at three different stages: (1) determining the three-band model parameters for each cuprate with input from density functional theory (DFT), (2) reducing a three-band model to a single-band model with DMRG-computed natural orbitals, and (3) transforming a single-band Hubbard model into a spin or t-J model using DMRG ground states and unitary circuits. The proposed framework provides a systematic and broadly applicable approach for deriving effective Hamiltonians in strongly correlated systems.