A practical guide to density matrix embedding theory in quantum chemistry

Abstract

Density matrix embedding theory (DMET) provides a theoretical framework to treat finite fragments in the presence of a surrounding molecular or bulk environment, even when there is significant correlation or entanglement between the two. In this work, we give a practically oriented and explicit description of the numerical and theoretical formulation of DMET. We also describe in detail how to perform self-consistent DMET optimizations. We explore different embedding strategies with and without a self-consistency condition in hydrogen rings, beryllium rings, and a sample S${}_{\text{N}}$2 reaction. The source code for the calculations in this work can be obtained from \url{https://github.com/sebwouters/qc-dmet}.

41 pages, 10 figures

References in corpus (6)

• The density matrix renormalization group for ab initio quantum chemistry
• Multireference Correlation in Long Molecules with the Quadratic Scaling Density Matrix Renormalization Group
• Dynamical Mean-Field Theory for Quantum Chemistry
• Investigation of metal-insulator like transition through the ab initio density matrix renormalization group approach
• Cluster Density Matrix Embedding Theory for Quantum Spin Systems
• Geminal embedding scheme for optimal atomic basis set construction in correlated calculations

Cited by in corpus (114)

• The Variational Quantum Eigensolver: a review of methods and best practices
• Elucidating Reaction Mechanisms on Quantum Computers
• The Density Matrix Renormalization Group in Chemistry and Molecular Physics: Recent Developments and New Challenges
• Quantum embedding theories
• Automated construction of molecular active spaces from atomic valence orbitals
• Towards the solution of the many-electron problem in real materials: equation of state of the hydrogen chain with state-of-the-art many-body methods
• Solving Many-Electron Schrödinger Equation Using Deep Neural Networks
• Emerging quantum computing algorithms for quantum chemistry
• Quantum simulations of materials on near-term quantum computers
• Efficient Implementation of Ab Initio Quantum Embedding in Periodic Systems: Density Matrix Embedding Theory
• A general second order complete active space self-consistent-field solver for large-scale systems
• Quantum Embedding Theory for Strongly-correlated States in Materials
• Exactly-embedded multiconfigurational self-consistent field theory using density matrix embedding: the localized active space self-consistent field method
• Quantum-centric Supercomputing for Materials Science: A Perspective on Challenges and Future Directions
• Quantum simulation with hybrid tensor networks
• Time-step targeting time-dependent and dynamical density matrix renormalization group algorithms with ab initio Hamiltonians
• Can Density Matrix Embedding Theory with the Complete Activate Space Self-Consistent Field Solver Describe Single and Double Bond Breaking in Molecular Systems?
• Green's function formulation of quantum defect embedding theory
• Systematic electronic structure in the cuprate parent state from quantum many-body simulations
• Efficient Formulation of Ab Initio Quantum Embedding in Periodic Systems: Dynamical Mean-Field Theory
• The Variational Localized Active Space Self-Consistent Field Method
• Toward Practical Quantum Embedding Simulation of Realistic Chemical Systems on Near-term Quantum Computers
• Quantum Computational Quantification of Protein-Ligand Interactions
• Systematic improvability in quantum embedding for real materials
• Rigorous wave function embedding with dynamical fluctuations
• Ground-state phase diagram of the three-band Hubbard model from density matrix embedding theory
• Dynamical Mean Field Theory, Density-Matrix Embedding Theory and Rotationally Invariant Slave Bosons: a Unified Perspective
• Simulating the electronic structure of spin defects on quantum computers
• Cluster size convergence of the density matrix embedding theory and its dynamical cluster formulation: a study with an auxiliary-field quantum Monte Carlo solver
• Orbital transformations to reduce the 1-norm of the electronic structure Hamiltonian for quantum computing applications
• Generalization of intrinsic orbitals to Kramers-paired quaternion spinors, molecular fragments and valence virtual spinors
• Energy-weighted density matrix embedding of open correlated chemical fragments
• Rotationally invariant slave-boson and density matrix embedding theory: A unified framework and a comparative study on the 1D and 2D Hubbard Model
• Fully Algebraic and Self-consistent Effective Dynamics in a Static Quantum Embedding
• Ab initio Quantum Simulation of Strongly Correlated Materials with Quantum Embedding
• First-principles Studies of Strongly Correlated States in Defect Spin Qubits in Diamond
• Perturbative quantum simulation
• Ultrafast ab-initio Quantum Chemistry Using Matrix Product States
• Periodic Local Coupled-Cluster Theory for Insulators and Metals
• Five years of density matrix embedding theory
• The Polarizable Embedding Density Matrix Renormalization Group Method
• Making Many-Body Interactions Nearly Pairwise Additive: The Polarized Many-Body Expansion Approach
• Projected Density Matrix Embedding Theory with Applications to the Two-Dimensional Hubbard Model
• Quantum Information-Assisted Complete Active Space Optimization (QICAS)
• Site-Occupation Embedding Theory using Bethe Ansatz Local Density Approximations
• Block product density matrix embedding theory for strongly correlated spin systems
• On the effective reconstruction of expectation values from ab initio quantum embedding
• Householder transformed density matrix functional embedding theory
• Rigorous screened interactions for realistic correlated electron systems
• Accuracy of ghost-rotationally-invariant slave-boson and dynamical mean field theory as a function of the impurity-model bath size
• Analysis of Electron Correlation Effects in Strongly Correlated Systems (${\mathrm{N}}_2$ and ${\mathrm{N}}_2^{+}$) by applying DMRG and Quantum Information Theory
• Incremental Embedding: A Density Matrix Embedding Scheme for Molecules
• Coupled cluster and perturbation theories based on a cluster mean-field reference applied to strongly correlated spin systems
• Extending Density Matrix Embedding: A Static Two-Particle Theory
• Dealing with the exponential wall in electronic structure calculations
• Bootstrap Embedding on a Quantum Computer
• Enhancing robustness and efficiency of density matrix embedding theory via semidefinite programming and local correlation potential fitting
• Fock space embedding theory for strongly correlated topological phases
• Compound-tunable embedding potential method and its application to fersmite crystal
• Fault-tolerant quantum algorithms for quantum molecular systems: A survey
• Projected site-occupation embedding theory
• Phase diagram of the square lattice Hubbard model with Rashba-type antisymmetric spin-orbit coupling
• Multi-site Reaction Dynamics Through Multi-fragment Density Matrix Embedding
• Unbiasing Fermionic Auxiliary-Field Quantum Monte Carlo with Matrix Product State Trial Wavefunctions
• Triply efficient shadow tomography
• Advances in Quantum Defect Embedding Theory
• Tensor network influence functionals in the continuous-time limit: connections to quantum embedding, bath discretization, and higher-order time propagation
• On-Premises Superconducting Quantum Computer for Education and Research
• A multi-fragment real-time extension of projected density matrix embedding theory: Non-equilibrium electron dynamics in extended systems
• Efficient Compression Of The Environment Of An Open Quantum System
• Interacting-bath dynamical embedding for capturing non-local electron correlation in solids
• Symmetry-projected cluster mean-field theory applied to spin systems
• Quantum embedding of multi-orbital fragments using the Block-Householder-transformation
• Local Potential Functional Embedding Theory: A Self-Consistent Flavor of Density Functional Theory for Lattices without Density Functionals
• High ground state overlap via quantum embedding methods
• Challenges with relativistic GW calculations in solids and molecules
• A unified density-matrix functional construction of quantum baths in density matrix embedding theory beyond the mean-field approximation
• Derivation of the Ghost Gutzwiller Approximation from Quantum Embedding principles: the Ghost Density Matrix Embedding Theory
• Quantum embedding for molecules using auxiliary particles -- The ghost Gutzwiller Ansatz
• Entanglement spectrum as a marker for phase transitions in the density embedding theory for interacting spinless fermionic models
• Frequency-dependent and algebraic bath states for a Dynamical Mean-Field Theory with compact support
• Comparative study of the density matrix embedding theory for the Hubbard models
• Multiple impurities and combined local density approximations in Site-Occupation Embedding Theory
• Simple embedding scheme for the spectral properties of the Single-Impurity Anderson Model
• ByteQC: GPU-Accelerated Quantum Chemistry Package for Large-Scale Systems
• FragPT2: Multi-Fragment Wavefunction Embedding with Perturbative Interactions
• Unitary transformations within density matrix embedding approaches: A novel perspective on the self-consistent scheme for electronic structure calculation
• Fragment quantum embedding using the Householder transformation: a multi-state extension based on ensembles
• Quantification of electron correlation effects - Quantum Information Theory versus Method of Increments
• Large-scale Efficient Molecule Geometry Optimization with Hybrid Quantum-Classical Computing
• Simulating optically-active spin defects with a quantum computer
• Quantum Computing in Pharma: A Multilayer Embedding Approach for Near Future Applications
• On the pure state $v$-representability of density matrix embedding theory
• Extending Quantum Computing through Subspace, Embedding and Classical Molecular Dynamics Techniques
• Local Potential Functional Embedding Theory of Molecular Systems: Localized Orbital-Based Embedding from an Exact Density-Functional Perspective
• Site-occupation--Green's function embedding theory: A density-functional approach to dynamical impurity solvers
• Encoded probabilistic imaginary-time evolution on a trapped-ion quantum computer for ground and excited states of spin qubits
• Extending the Gutzwiller approximation to intersite interactions
• Exploration of Quantum Computing in Materials Discovery for Direct Air Capture Applications
• Demonstration of system-bath physics on a gate-based quantum computer
• Density Matrix Embedding Theory and Strongly Correlated Lattice Systems
• Configuration interaction approaches for solving quantum impurity models
• Optimizing Electronic Structure Simulations on a Trapped-ion Quantum Computer using Problem Decomposition
• Solving the Hubbard model using density matrix embedding theory and the variational quantum eigensolver
• A versatile unitary transformation framework for an optimal bath construction in density-matrix based quantum embedding approaches
• Ab Initio Many Body Quantum Embedding and Local Correlation in Crystalline Materials using Interpolative Separable Density Fitting
• Degenerate orbital effect in a three orbital periodic Anderson model
• Active Learning approach to simulations of Strongly Correlated Matter with the Ghost Gutzwiller Approximation
• Theory of interaction-induced charge order in CrSBr
• Ghost Embedding Bridging Chemistry and One-Body Theories
• Towards Excitations and Dynamical Quantities in Correlated Lattices with Density Matrix Embedding Theory
• Electronic Structure for Multielectronic Molecules Near a Metal Surface
• Ensemble density functional theory of excited states: Exact N-centered formalism and practical opportunities
• Anderson localization: a density matrix approach