The Density Matrix Renormalization Group in Chemistry and Molecular Physics: Recent Developments and New Challenges

Abstract

In the past two decades, the density matrix renormalization group (DMRG) has emerged as an innovative new method in quantum chemistry relying on a theoretical framework very different from that of traditional electronic structure approaches. The development of the quantum chemical DMRG has been remarkably fast: it has already become one of the reference approaches for large-scale multiconfigurational calculations. This perspective discusses the major features of DMRG, highlighting its strengths and weaknesses also in comparison to other novel approaches. The method is presented following its historical development, starting from its original formulation up to its most recent applications. Possible routes to recover dynamical correlation are discussed in detail. Emerging new fields of applications of DMRG are explored, in particular its time-dependent formulation and the application to vibrational spectroscopy.

25 pages, 2 figures

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• Extension of selected configuration interaction for transcorrelated methods
• A new form of transcorrelated Hamiltonian inspired by range-separated DFT
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• Finite-temperature many-body perturbation theory for electrons: Algebraic recursive definitions, second-quantized derivation, linked-diagram theorem, general-order algorithms, grand canonical and canonical ensembles
• Minimal matrix product states and generalizations of mean-field and geminal wavefunctions
• Towards Efficient Quantum Computing for Quantum Chemistry: Reducing Circuit Complexity with Transcorrelated and Adaptive Ansatz Techniques
• Inversion symmetry of singular values and a new orbital ordering method in tensor train approximations for quantum chemistry
• Exact matrix product state representation and convergence of a fully correlated electronic wavefunction in the infinite basis limit
• Further Development of iCIPT2 for Strongly Correlated Electrons
• Modeling the dynamics of quantum systems coupled to large dimensional baths using effective energy states
• Solving intractable chemical problems by tensor decomposition