A tensor network view of multilayer multiconfiguration time-dependent Hartree methods

Abstract

The multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) method and the density matrix renormalization group (DMRG) are powerful workhorses applied mostly in different scientific fields. Although both methods are based on tensor network states, very different mathematical languages are used for describing them. This severely limits knowledge transfer and sometimes leads to re-inventions of ideas well known in the other field. Here, we review ML-MCTDH and DMRG theory using both MCTDH expressions and tensor network diagrams. We derive the ML-MCTDH equations of motions using diagrams and compare them with time-dependent and time-independent DMRG algorithms. We further review two selected recent advancements. The first advancement is related to optimizing unoccupied single-particle functions in MCTDH, which corresponds to subspace enrichment in the DMRG. The second advancement is related to finding optimal tree structures and on highlighting similarities and differences of tensor networks used in MCTDH and DMRG theories. We hope that this contribution will foster more fruitful cross-fertilization of ideas between ML-MCTDH and DMRG.

References in corpus (83)

• The density-matrix renormalization group in the age of matrix product states
• The density-matrix renormalization group
• Efficient classical simulation of slightly entangled quantum computations
• A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
• Efficient simulation of one-dimensional quantum many-body systems
• Real time evolution using the density matrix renormalization group
• Entanglement renormalization
• Thermodynamic limit of the density matrix renormalization for the spin-1 Heisenberg chain
• A class of quantum many-body states that can be efficiently simulated
• Time-dependent variational principle for quantum lattices
• Unifying time evolution and optimization with matrix product states
• Matrix product states represent ground states faithfully
• Time-evolution methods for matrix-product states
• Criticality, the area law, and the computational power of PEPS
• Classical simulation of quantum many-body systems with a tree tensor network
• Ab Initio Quantum Chemistry using the Density Matrix Renormalization Group
• Renormalization algorithms for Quantum-Many Body Systems in two and higher dimensions
• Low-Rank Tensor Networks for Dimensionality Reduction and Large-Scale Optimization Problems: Perspectives and Challenges PART 1
• Hand-waving and Interpretive Dance: An Introductory Course on Tensor Networks
• Multilayer multi-configuration time-dependent Hartree method: implementation and applications to a Henon-Heiles Hamiltonian and to pyrazine
• Matrix product operator representations
• The multi-configurational time-dependent Hartree method for bosons: Many-body dynamics of bosonic systems
• Tensor product methods and entanglement optimization for ab initio quantum chemistry
• Variational optimization algorithms for uniform matrix product states
• Controlling the accuracy of the density matrix renormalization group method: The Dynamical Block State Selection approach
• Simulating Strongly Correlated Quantum Systems with Tree Tensor Networks
• Density matrix renormalization group algorithms with a single center site
• Role of excited states in the splitting dynamics of interacting Bose-Einstein condensates when ramping-up a barrier
• Quantum information analysis of electronic states at different molecular structures
• Tangent-space methods for uniform matrix product states
• CheMPS2: a free open-source spin-adapted implementation of the density matrix renormalization group for ab initio quantum chemistry
• Time-step targetting methods for real-time dynamics using DMRG
• Time integration of tensor trains
• A Strictly Single-Site DMRG Algorithm with Subspace Expansion
• Full dimensional (15D) quantum-dynamical simulation of the protonated water-dimer I: Hamiltonian setup and analysis of the ground vibrational state
• Efficient Tree Tensor Network States (TTNS) for Quantum Chemistry: Generalizations of the Density Matrix Renormalization Group Algorithm
• Multiconfigurational time-dependent Hartree approaches for indistinguishable particles
• Time Dependent Variational Principle with Ancillary Krylov Subspace
• Isometric Tensor Network States in Two Dimensions
• Large-scale quantum-dynamics with matrix product states
• Approximating strongly correlated spin and fermion wavefunctions with correlator product states
• Block2: a comprehensive open source framework to develop and apply state-of-the-art DMRG algorithms in electronic structure and beyond
• QC-DMRG study of the ionic--neutral curve crossing of LiF
• Time-dependent variational principle in matrix-product state manifolds: pitfalls and potential
• Time-dependent Density Matrix Renormalization Group Quantum Dynamics for Realistic Chemical Systems
• Complete-Graph Tensor Network States: A New Fermionic Wave Function Ansatz for Molecules
• Unconstrained Tree Tensor Network: An adaptive gauge picture for enhanced performance
• Multi-Layer Potfit: An Accurate Potential Representation for Efficient High-Dimensional Quantum Dynamics
• Time-step targeting time-dependent and dynamical density matrix renormalization group algorithms with ab initio Hamiltonians
• Computing vibrational eigenstates with tree tensor network states (TTNS)
• Targeted Excited State Algorithms
• T3NS: three-legged tree tensor network states
• Time Dependent Variational Principle for Tree Tensor Networks
• Error estimates for extrapolations with matrix-product states
• Multi-set matrix product state calculations reveal mobile Franck-Condon excitations under strong Holstein-type coupling
• Calculating vibrational spectra of molecules using tensor train decomposition
• Linear Response Theory for the Density Matrix Renormalization Group: Efficient Algorithms for Strongly Correlated Excited States
• The coupling of the hydrated proton to its first solvation shell
• Analytic response theory for the density matrix renormalization group
• The Thouless theorem for matrix product states and subsequent post-density matrix renormalization group methods
• Optimization of highly excited matrix product states with an application to vibrational spectroscopy
• Efficient molecular quantum dynamics in coordinate and phase space using pruned bases
• Matrix product state formulation of the multiconfiguration time-dependent Hartree theory
• Conversion of projected entangled pair states into a canonical form
• Dynamical pruning of the multiconfiguration time-dependent Hartree method (DP-MCTDH): An efficient approach for multidimensional quantum dynamics
• Local-in-time error in variational quantum dynamics
• Automatic structural optimization of tree tensor networks
• Concatenated tensor network states
• Controlled bond expansion for DMRG ground state search at single-site costs
• Stochastic Adaptive Single-Site Time-Dependent Variational Principle
• Heisenberg antiferromagnet on Cayley trees: low-energy spectrum and even/odd site imbalance
• Flexible DMRG-based framework for anharmonic vibrational calculations
• Entanglement bipartitioning and tree tensor networks
• Tangent space formulation of the Multi-Configuration Time-Dependent Hartree equations of motion: The projector-splitting algorithm revisited
• Accuracy of Potfit-based potential representations and its impact on the performance of (ML-)MCTDH
• Truncated many-body dynamics of interacting bosons: A variational principle with error monitoring
• Minimal matrix product states and generalizations of mean-field and geminal wavefunctions
• Projector formalism for kept and discarded spaces of matrix product states
• Boosting Vector Calculus with the Graphical Notation
• Massively Parallel Tensor Network State Algorithms on Hybrid CPU-GPU Based Architectures
• Exploring Disordered Quantum Spin Models with a Multi-Layer Multi-Configurational Approach
• Least Action Principle for the Real-Time Density Matrix Renormalization Group
• A parallel rank-adaptive integrator for dynamical low-rank approximation

Cited by in corpus (19)

• Roadmap for Molecular Benchmarks in Nonadiabatic Dynamics
• Time-dependent variational principle with controlled bond expansion for matrix product states
• ACE: A general-purpose non-Markovian open quantum systems simulation toolkit based on process tensors
• Optimal Tree Tensor Network Operators for Tensor Network Simulations: Applications to Open Quantum Systems
• 2500 vibronic eigenstates of the NO${}_3$ radical
• Benchmarking vibrational spectra: 5000 accurate eigenstates of acetonitrile using tree tensor network states
• Extending Non-Perturbative Simulation Techniques for Open-Quantum Systems to Excited-State Proton Transfer and Ultrafast Non-Adiabatic Dynamics
• Quantum Algorithm for Vibronic Dynamics: Case Study on Singlet Fission Solar Cell Design
• Multidimensional quantum dynamics with explicitly correlated Gaussian wave packets using Rothe's method
• Simulating real-time molecular electron dynamics efficiently using the time-dependent density matrix renormalization group
• QCMaquis 4.0: Multi-Purpose Electronic, Vibrational, and Vibronic Structure and Dynamics Calculations with the Density Matrix Renormalization Group
• Computing excited eigenstates using inexact Lanczos methods and tree tensor network states
• Trotter simulation of vibrational Hamiltonians on a quantum computer
• Improving accuracy of tree-tensor network approach by optimization of network structure
• Ab-Initio Approach to Many-Body Quantum Spin Dynamics
• Solving intractable chemical problems by tensor decomposition
• Process Tensor Approaches to Non-Markovian Quantum Dynamics
• paces: Parallelized Application of Co-Evolving Subspaces, a method for computing quantum dynamics on GPUs
• Accurate, full-dimensional computations of thousands of complex vibrational eigenstates with tree tensor network states