From real materials to model Hamiltonians with density matrix downfolding

Abstract

Due to advances in computer hardware and new algorithms, it is now possible to perform highly accurate many-body simulations of realistic materials with all their intrinsic complications. The success of these simulations leaves us with a conundrum: how do we extract useful physical models and insight from these simulations? In this article, we present a formal theory of downfolding--extracting an effective Hamiltonian from first-principles calculations. The theory maps the downfolding problem into fitting information derived from wave functions sampled from a low-energy subspace of the full Hilbert space. Since this fitting process most commonly uses reduced density matrices, we term it density matrix downfolding (DMD).

24 pages, 12 figures; Huihuo Zheng and Hitesh J. Changlani contributed equally to this work

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• Excited states in variational Monte Carlo using a penalty method
• Density-matrix-renormalization-group-based downfolding of the three-band Hubbard model: the importance of density-assisted hopping
• Spin--lattice coupling and the emergence of the trimerized phase in the $S=1$ Kagome antiferromagnet Na${}_2$Ti${}_3$Cl${}_8$
• Magnetism and charge order in the honeycomb lattice
• Rigorous screened interactions for realistic correlated electron systems
• PyQMC: an all-Python real-space quantum Monte Carlo module in PySCF
• Magnetic Susceptibility and Simulated Neutron Signal in the 2D Hubbard Model
• Simultaneous fermion and exciton condensations from a model Hamiltonian
• Prediction for the singlet-triplet excitation energy for the spinel MgTi${}_2$O${}_4$ using first-principles diffusion Monte Carlo
• Charge conserving approximation for excitation properties of crystalline materials
• Simulation Methodology for Electron Transfer in CMOS Quantum Dots
• Compressing Hamiltonians with ab initio downfolding for simulating strongly-correlated materials on quantum computers
• The Future of the Correlated Electron Problem
• Renormalized density matrix downfolding: A rigorous framework in learning emergent models from ab initio many-body calculations
• Classical Benchmarks for Variational Quantum Eigensolver Simulations of the Hubbard Model
• Origin and stability of generalized Wigner crystallinity in triangular moiré systems
• Unsupervised Learning of Effective Quantum Impurity Models
• Ground-State-Based Model Reduction with Unitary Circuits
• Effective spin-orbit models using correlated first-principles wave functions
• Theory of ab initio downfolding with arbitrary range electron-phonon coupling