One-dimensional Continuum Electronic Structure with the Density Matrix Renormalization Group and Its Implications For Density Functional Theory

Abstract

We extend the density matrix renormalization group to compute exact ground states of continuum many-electron systems in one dimension with long-range interactions. We find the exact ground state of a chain of 100 strongly correlated artificial hydrogen atoms. The method can be used to simulate 1d cold atom systems and to study density functional theory in an exact setting. To illustrate, we find an interacting, extended system which is an insulator but whose Kohn-Sham system is metallic.

5 pages, 4 figures. Published version, including new section on exact Kohn-Sham gap of a Mott insulator

References in corpus (9)

• One dimensional Bosons: From Condensed Matter Systems to Ultracold Gases
• Majorana Fermions in Equilibrium and Driven Cold Atom Quantum Wires
• From density-matrix renormalization group to matrix product states
• Continuous Matrix Product States for Quantum Fields
• Stripes in the two-dimensional t-J model with infinite projected entangled-pair states
• Multireference Correlation in Long Molecules with the Quadratic Scaling Density Matrix Renormalization Group
• Ground-State Energy and Spin Gap of Spin-1/2 Kagome Heisenberg Antiferromagnetic Clusters: Large Scale Exact Diagonalization Results
• Density functional theory beyond the linear regime: Validating adiabatic LDA
• Multigrid Algorithms for Tensor Network States

Cited by in corpus (53)

• Kohn-Sham equations as regularizer: building prior knowledge into machine-learned physics
• Strong correlation in Kohn-Sham density functional theory
• Pure density functional for strong correlations and the thermodynamic limit from machine learning
• The Hubbard Dimer: A density functional case study of a many-body problem
• Real-Space Parallel Density Matrix Renormalization Group
• Can Density Matrix Embedding Theory with the Complete Activate Space Self-Consistent Field Solver Describe Single and Double Bond Breaking in Molecular Systems?
• Quantum Flutter: Signatures and Robustness
• Kohn-Sham calculations with the exact functional
• Continuous Matrix Product States for Quantum Fields: an Energy Minimization Algorithm
• Kohn-Sham density functional theory for quantum wires in arbitrary correlation regimes
• Wigner localization in quantum dots from Kohn-Sham density functional theory without symmetry breaking
• Guaranteed convergence of the Kohn-Sham equations
• Quantum distillation and confinement of vacancies in a doublon sea
• Towards the Kantorovich dual solution for strictly correlated electrons in atoms and molecules
• Sliced Basis Density Matrix Renormalization Group for Electronic Structure
• Quantum Shock Waves and Population Inversion in Collisions of Ultracold Atomic Clouds
• One Dimensional Mimicking of Electronic Structure: The Case for Exponentials
• Universal nature of different methods of obtaining the exact Kohn-Sham exchange-correlation potential for a given density
• Hybrid grid/basis set discretizations of the Schrödinger equation
• High-density correlation energy expansion of the one-dimensional uniform electron gas
• Moiré versus Mott: Incommensuration and Interaction in One-Dimensional Bichromatic Lattices
• Chemistry in One Dimension
• Augmenting Density Matrix Renormalization Group with Disentanglers
• Ab initio electronic density in solids by many-body plane-wave auxiliary-field quantum Monte Carlo calculations
• Systematic construction of density functionals based on matrix product state computations
• Continuous matrix product states for non-relativistic quantum fields: a lattice algorithm for inhomogeneous systems
• Direct calculation of the Entanglement Spectrum in Quantum Monte Carlo with application to \textit{ab initio} Hamiltonians
• Accurate Kohn-Sham auxiliary system from the ground state density of solids
• Accurate effective potential for density amplitude and the corresponding Kohn-Sham exchange-correlation potential calculated from approximate wavefunctions
• Exact exchange-correlation potential of a ionic Hubbard model with a free surface
• Efficient representation of long-range interactions in tensor network algorithms
• Solving lattice density functionals close to the Mott regime
• Dependence of structure factor and correlation energy on the width of electron wires
• Density functionals and Kohn-Sham potentials with minimal wavefunction preparations on a quantum computer
• On the generalization of the exponential basis for tensor network representations of long-range interactions in two and three dimensions
• Molecular electronic structure in one-dimensional Coulomb systems
• Multiple phase separation in one-dimensional mixtures of mass- and population-imbalanced attractive Fermi gases
• Density functional theory with adaptive pair density
• Density-Matrix Renormalization Group for Continuous Quantum Systems
• Non-existence of Taylor expansion in time due to cusps
• Variational adiabatic transport of tensor networks
• Approximate Quantum Compiling for Quantum Simulation: A Tensor Network based approach
• Chemical accuracy from small, system-adapted basis functions
• The Nonequilibrium Many-Body Problem as a paradigm for extreme data science
• The matrix product approximation for the dynamic cavity method
• Numerical continuum tensor networks in two dimensions
• Using random numbers to obtain Kohn-Sham potential for a given density
• Quantum Phase Transitions in Long-Range Interacting Hyperuniform Spin Chains in a Transverse Field
• Building bridges: matching density functional theory with experiment
• Predicting fermionic densities using a Projected Quantum Kernel method
• Asymptotics of eigenvalue sums when some turning points are complex
• A tensor network representation of path integrals: Implementation and analysis
• Lies My Teacher Told Me About Density Functional Theory: Seeing Through Them with the Hubbard Dimer