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We review the variational principle in the density matrix renormalization group (DMRG) method, which maximizes an approximate partition function within a restricted degrees of freedom; at zero temperature, DMRG mini- mizes the ground state…

Statistical Mechanics · Physics 2009-10-28 T. Nishino , K. Okunishi

Facilitated by a rigorous partitioning of a molecular system's orbital basis into two fundamental subspaces - a reference and an expansion space, both with orbitals of unspecified occupancy - we generalize our recently introduced many-body…

Chemical Physics · Physics 2019-12-12 Janus J. Eriksen , Jürgen Gauss

We have implemented internally contracted complete active space second order perturbation theory (CASPT2) with the density matrix renormalization group (DMRG) as active space solver [Y. Kurashige and T. Yanai, J. Chem. Phys. 135, 094104…

Chemical Physics · Physics 2016-08-09 Sebastian Wouters , Veronique Van Speybroeck , Dimitri Van Neck

Relativistic magnetic hyperfine interaction Hamiltonian based on the Douglas-Kroll-Hess (DKH) theory up to the second order is implemented within the ab initio multireference methods including spin-orbit coupling in the Molcas/OpenMolcas…

Materials Science · Physics 2023-09-19 Aleksander L. Wysocki , Kyungwha Park

In the realm of quantum chemistry, the accurate prediction of electronic structure and properties of nanostructures remains a formidable challenge. Density Functional Theory (DFT) and Density Matrix Renormalization Group (DMRG) have emerged…

Strongly Correlated Electrons · Physics 2024-02-21 T. Pauletti , M. Sanino , L. Gimenes , I. M. Carvalho , V. V. França

The accurate resolution of the chemical properties of strongly correlated systems, such as biradicals, requires the use of electronic structure theories that account for both multi-reference as well as dynamic correlation effects. A variety…

Chemical Physics · Physics 2023-01-03 Jan-Niklas Boyn , David A. Mazziotti

We investigate the application of the Density Matrix Renormalization Group (DMRG) to the Hubbard model in momentum-space. We treat the one-dimensional models with dispersion relations corresponding to nearest-neighbor hopping and $1/r$…

Strongly Correlated Electrons · Physics 2009-11-07 Satoshi Nishimoto , Eric Jeckelmann , Florian Gebhard , Reinhard M. Noack

Data-Driven Response Regime Exploration and Identification (DR$^2$EI) is a novel and fully data-driven method for identifying and classifying response regimes of a dynamical system without requiring human intervention. This approach is a…

Systems and Control · Electrical Eng. & Systems 2023-04-13 Maor Farid

The development of polynomial cost solvers for correlated quantum impurity models, with controllable errors, is a central challenge in quantum many-body physics, where these models find applications ranging from nano-science to the…

Strongly Correlated Electrons · Physics 2012-12-21 Dominika Zgid , Emanuel Gull , Garnet Chan

Hydrogen tunneling is an important process that impacts reaction rates and molecular spectra. Describing and understanding this process requires a quantum mechanical treatment of the transferring hydrogen. The nuclear-electronic orbital…

Chemical Physics · Physics 2025-07-14 Rachel J. Stein , Christopher L. Malbon , Sharon Hammes-Schiffer

We reformulate the density matrix renormalization group method (DMRG) in terms of a single block, instead of the standard left and right blocks used in the construction of the superblock. This version of the DMRG, which we call the puncture…

Condensed Matter · Physics 2009-10-31 M. A. Martin-Delgado , J. Rodriguez-Laguna , G. Sierra

We implement an efficient numerical method to calculate response functions of complex impurities based on the Density Matrix Renormalization Group (DMRG) and use it as the impurity-solver of the Dynamical Mean Field Theory (DMFT). This…

Strongly Correlated Electrons · Physics 2017-11-27 Y. Núñez Fernández , K. Hallberg

We present a second-order N-electron valence state perturbation theory (NEVPT2) based on a density matrix renormalization group (DMRG) reference wave function that exploits a Cholesky decomposition of the two-electron repulsion integrals…

Chemical Physics · Physics 2017-03-07 Leon Freitag , Stefan Knecht , Celestino Angeli , Markus Reiher

We extend the recently proposed heat-bath configuration interaction (HCI) method [Holmes, Tubman, Umrigar, J. Chem. Theory Comput. 12, 3674 (2016)], by introducing a semistochastic algorithm for performing multireference Epstein-Nesbet…

Chemical Physics · Physics 2017-03-20 Sandeep Sharma , Adam Holmes , Guillaume Jeanmairet , Ali Alavi , C. J. Umrigar

We present a detailed discussion of a novel dynamical renormalization group scheme: the Dynamically Driven Renormalization Group (DDRG). This is a general renormalization method developed for dynamical systems with non-equilibrium critical…

Condensed Matter · Physics 2009-10-28 Alessandro Vespignani , Stefano Zapperi , Vittorio Loreto

The generalization of Density Matrix Renormalization Group (DMRG) approach as implemented in quantum chemistry, to the case of non-orthogonal orbitals is carefully analyzed. This generalization is attractive from the physical point of view…

Strongly Correlated Electrons · Physics 2007-05-23 A. O. Mitrushenkov , Guido Fano , Roberto Linguerri , Paolo Palmieri

The purpose of this paper is (i) to present a generic and fully functional implementation of the density-matrix renormalization group (DMRG) algorithm, and (ii) to describe how to write additional strongly-correlated electron models and…

Strongly Correlated Electrons · Physics 2015-05-13 G. Alvarez

In this work, we extend selected configuration interaction (SCI) methods beyond energies and expectation values by introducing a linear response (LR) framework for molecular response properties. Existing SCI approaches are capable of…

Chemical Physics · Physics 2025-11-24 Peter Reinholdt , Erik Kjellgren , Jacob Kongsted

The combinatorial scaling of configuration interaction (CI) has long restricted its applicability to only the simplest molecular systems. Here, we report the first numerically exact CI calculation exceeding one quadrillion ($10^{15}$)…

Chemical Physics · Physics 2025-12-16 Agam Shayit , Can Liao , Shiv Upadhyay , Hang Hu , Tianyuan Zhang , Eugene DePrince , Chao Yang , Xiaosong Li

Obtaining accurate representations of the eigenstates of an array of coupled superconducting qubits is a crucial step in the design of circuit quantum electrodynamics (QED)-based quantum processors. However, exact diagonalization of the…