Transcorrelated Density Matrix Renormalization Group

Abstract

We introduce the transcorrelated Density Matrix Renormalization Group (tcDMRG) theory for the efficient approximation of the energy for strongly correlated systems. tcDMRG encodes the wave function as a product of a fixed Jastrow or Gutzwiller correlator and a matrix product state. The latter is optimized by applying the imaginary-time variant of time-dependent (TD) DMRG to the non-Hermitian transcorrelated Hamiltonian. We demonstrate the efficiency of tcDMRG at the example of the two-dimensional Fermi-Hubbard Hamiltonian, a notoriously difficult target for the DMRG algorithm, for different sizes, occupation numbers, and interaction strengths. We demonstrate fast energy convergence of tcDMRG, which indicates that tcDMRG could increase the efficiency of standard DMRG beyond quasi-monodimensional systems and provides a generally powerful approach toward the dynamic correlation problem of DMRG.

31 pages, 4 figures, 4 tables

References in corpus (60)

• The density-matrix renormalization group in the age of matrix product states
• Efficient simulation of one-dimensional quantum many-body systems
• An Area Law for One Dimensional Quantum Systems
• Unifying time evolution and optimization with matrix product states
• Time-evolution methods for matrix-product states
• Ab Initio Quantum Chemistry using the Density Matrix Renormalization Group
• Long-range/short-range separation of the electron-electron interaction in density functional theory
• Semistochastic Heat-bath Configuration Interaction method: selected configuration interaction with semistochastic perturbation theory
• Studying Two Dimensional Systems With the Density Matrix Renormalization Group
• Matrix product operator representations
• The Density Matrix Renormalization Group in Chemistry and Molecular Physics: Recent Developments and New Challenges
• A deterministic alternative to the full configuration interaction quantum Monte Carlo method
• The density matrix renormalization group for ab initio quantum chemistry
• Tensor product methods and entanglement optimization for ab initio quantum chemistry
• Tensor network states and algorithms in the presence of a global U(1) symmetry
• Measuring orbital interaction using quantum information theory
• Density matrix renormalization group algorithms with a single center site
• Quantum information analysis of electronic states at different molecular structures
• An Efficient Matrix Product Operator Representation of the Quantum-Chemical Hamiltonian
• N-electron valence state perturbation theory based on a density matrix renormalization group reference function, with applications to the chromium dimer and poly-p-phenylene vinylene oligomer
• Time integration of tensor trains
• The Ground State Electronic Energy of Benzene
• Generic Construction of Efficient Matrix Product Operators
• Hybrid stochastic-deterministic calculation of the second-order perturbative contribution of multireference perturbation theory
• Multi-reference perturbation theory with Cholesky decomposition for the density matrix renormalization group
• New Approaches for ab initio Calculations of Molecules with Strong Electron Correlation
• Large-scale quantum-dynamics with matrix product states
• Density Matrix Renormalization Group and Reaction-Diffusion Processes
• Density Matrix Renormalization Group with Efficient Dynamical Electron Correlation Through Range Separation
• A flexible multi-reference perturbation theory by minimizing the Hylleraas functional with matrix product states
• autoCAS: a program for fully automated multi-configurational calculations
• Coupled cluster method with single and double excitations tailored by matrix product state wave functions
• Benchmark study of the two-dimensional Hubbard model with auxiliary-field quantum Monte Carlo method
• Matrix Product State applications for the ALPS project
• Hybrid-space density matrix renormalization group study of the doped two-dimensional Hubbard model
• Symmetry in Auxiliary-Field Quantum Monte Carlo Calculations
• Direct comparison of many-body methods for realistic electronic Hamiltonians
• Virtual orbital many-body expansions: A possible route towards the full configuration interaction limit
• Applying Adaptive Time-Dependent DMRG to Calculate the Conductance of Strongly Correlated Nanostructures
• Tensor operators: constructions and applications for long-range interaction systems
• Time-step targeting time-dependent and dynamical density matrix renormalization group algorithms with ab initio Hamiltonians
• DMRG-CASPT2 study of the longitudinal static second hyperpolarizability of all-trans polyenes
• Density matrix renormalization group on a cylinder in mixed real and momentum space
• Vibrational Density Matrix Renormalization Group
• Quantum simulation of electronic structure with a transcorrelated Hamiltonian: improved accuracy with a smaller footprint on the quantum computer
• Compact numerical solutions to the two-dimensional repulsive Hubbard model obtained via non-unitary similarity transformations
• A General Automatic Method for Optimal Construction of Matrix Product Operators Using Bipartite Graph Theory
• Similarity transformation of the electronic Schrödinger equation via Jastrow factorisation
• Curing basis-set convergence of wave-function theory using density-functional theory: a systematically improvable approach
• Optimization of highly excited matrix product states with an application to vibrational spectroscopy
• Dynamical phase behavior of the single- and multi-lane asymmetric simple exclusion process via matrix product states
• Entanglement structure of the Hubbard model in momentum space
• Dynamical Phase Transitions in a 2D Classical Nonequilibrium Model via 2D Tensor Networks
• Ultrafast ab-initio Quantum Chemistry Using Matrix Product States
• Improving the accuracy of quantum computational chemistry using the transcorrelated method
• Further developments in correlator product states: deterministic optimization and energy evaluation
• Lie Algebraic Similarity Transformed Hamiltonians for Lattice Model Systems
• Multireference configuration interaction and perturbation theory without reduced density matrices
• Understanding repulsively mediated superconductivity of correlated electrons via massively parallel DMRG
• An efficient stochastic algorithm for the perturbative density matrix renormalization group in large active spaces

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• Machine learning for electronically excited states of molecules
• Block2: a comprehensive open source framework to develop and apply state-of-the-art DMRG algorithms in electronic structure and beyond
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• Tailored Coupled Cluster Theory in Varying Correlation Regimes
• Molecule-specific Uncertainty Quantification in Quantum Chemical Studies
• Electron Dynamics with the Time-Dependent Density Matrix Renormalization Group
• Optimizing Jastrow factors for the transcorrelated method
• Explicitly correlated electronic structure calculations with transcorrelated matrix product operators
• Incremental Treatments of the Full Configuration Interaction Problem
• xTC: An efficient treatment of three-body interactions in transcorrelated methods
• Transcorrelated coupled cluster methods. II. Molecular systems
• Studies on the Transcorrelated Method
• Nonunitary projective transcorrelation theory inspired by the F12 ansatz
• Towards Efficient Quantum Computing for Quantum Chemistry: Reducing Circuit Complexity with Transcorrelated and Adaptive Ansatz Techniques
• Orbital optimisation in xTC transcorrelated methods
• Compactification of Determinant Expansions via Transcorrelation
• Complete Active Space Iterative Coupled Cluster Theory
• TC++: First-principles calculation code for solids using the transcorrelated method
• Striking the Right Balance of Encoding Electron Correlation in the Hamiltonian and the Wavefunction Ansatz
• Tuning the entanglement growth in matrix-product-state evolution of quantum systems by nonunitary similarity transformations
• QCMaquis 4.0: Multi-Purpose Electronic, Vibrational, and Vibronic Structure and Dynamics Calculations with the Density Matrix Renormalization Group
• Non-iterative Triples for Transcorrelated Coupled Cluster Theory
• Fully self-consistent optimization of the Jastrow-Slater-type wave function using a similarity-transformed Hamiltonian
• Scaling up the transcorrelated density matrix renormalization group