The Experts below are selected from a list of 215382 Experts worldwide ranked by ideXlab platform
E. K. U. Gross - One of the best experts on this subject based on the ideXlab platform.
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Reduced Density Matrix Functional Theory at Finite Temperature: Theoretical Foundations
arXiv: Other Condensed Matter, 2012Co-Authors: Tim Baldsiefen, Attila Cangi, E. K. U. GrossAbstract:We present an ab-initio approach for grand canonical ensembles in thermal equilibrium with local or nonlocal external potentials based on the one-reduced Density Matrix. We show that equilibrium properties of a grand canonical ensemble are determined uniquely by the eq-1RDM and establish a variational principle for the grand potential with respect to its one-reduced Density Matrix. We further prove the existence of a Kohn-Sham system capable of reproducing the one-reduced Density Matrix of an interacting system at finite temperature. Utilizing this Kohn-Sham system as an unperturbed system, we deduce a many-body approach to iteratively construct approximations to the correlation contribution of the grand potential.
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Minimization procedure in reduced Density Matrix functional theory by means of an effective noninteracting system
arXiv: Other Condensed Matter, 2012Co-Authors: Tim Baldsiefen, E. K. U. GrossAbstract:In this work, we propose a self-consistent minimization procedure for functionals in reduced Density Matrix functional theory. We introduce an effective noninteracting system at finite temperature which is capable of reproducing the groundstate one-reduced Density Matrix of an interacting system at zero temperature. By introducing the concept of a temperature tensor the minimization with respect to the occupation numbers is shown to be greatly improved.
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Noncollinear spin-spiral phase for the uniform electron gas within reduced-Density-Matrix-functional theory
Physical Review B, 2010Co-Authors: F. G. Eich, Stefan Kurth, C. R. Proetto, Sandeep Sharma, E. K. U. GrossAbstract:The noncollinear spin-spiral Density wave of the uniform electron gas is studied in the framework of reduced-Density-Matrix-functional theory. For the Hartree-Fock approximation, which can be obtained as a limiting case of reduced-Density-Matrix-functional theory, Overhauser showed a long-time ago that the paramagnetic state of the electron gas is unstable with respect to the formation of charge- or spin-Density waves. Here we not only present a detailed numerical investigation of the spin-spiral Density wave in the Hartree-Fock approximation but also investigate the effects of correlations on the spin-spiral Density wave instability by means of a recently proposed Density-Matrix functional.
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Reduced Density Matrix functional for many-electron systems
Physical Review B, 2008Co-Authors: S. Sharma, Nektarios N. Lathiotakis, J. K. Dewhurst, E. K. U. GrossAbstract:Reduced Density Matrix functional theory for the case of solids is presented and an exchange-correlation functional based on a fractional power of the Density Matrix is introduced. We show that compared to other functionals, this produces more accurate behavior for total energies as a function of particle number for finite systems. Moreover, it captures the correct band-gap behavior for conventional semiconductors, as well as strongly correlated Mott insulators, where a gap is obtained in the absence of any magnetic ordering.
Peter E Blochl - One of the best experts on this subject based on the ideXlab platform.
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Density Matrix functionals from green s functions
Physical Review B, 2013Co-Authors: Peter E Blochl, Thomas Pruschke, Michael PotthoffAbstract:The exact reduced Density-Matrix functional is derived from the Luttinger-Ward functional of the single-particle Green's function. Thereby, a formal link is provided between diagrammatic many-body approaches using Green's functions on the one hand and theories based on many-body wave functions on the other. This link can be used to explicitly construct approximations for the Density-Matrix functional that are equivalent to standard diagrammatic resummation techniques and to nonperturbative dynamical mean field theory in particular. Contrary to functionals of the Green's function, the exact Density-Matrix functional is convex and thus provides a true minimum principle which facilitates the calculation of the grand potential and derived equilibrium properties. The benefits of the proposed Green's-function-based Density-Matrix functional theory for geometrical structure optimization of strongly correlated materials are discussed.
Katarzyna Pernal - One of the best experts on this subject based on the ideXlab platform.
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Reduced Density Matrix Functional Theory (RDMFT) and Linear Response Time-Dependent RDMFT (TD-RDMFT).
Density-Functional Methods for Excited States, 2015Co-Authors: Katarzyna Pernal, Klaas J. H. GiesbertzAbstract:Recent advances in reduced Density Matrix functional theory (RDMFT) and linear response time-dependent reduced Density Matrix functional theory (TD-RDMFT) are reviewed. In particular, we present various approaches to develop approximate Density Matrix functionals which have been employed in RDMFT. We discuss the properties and performance of most available Density Matrix functionals. Progress in the development of functionals has been paralleled by formulation of novel RDMFT-based methods for predicting properties of molecular systems and solids. We give an overview of these methods. The time-dependent extension, TD-RDMFT, is a relatively new theory still awaiting practical and generally useful functionals which would work within the adiabatic approximation. In this chapter we concentrate on the formulation of TD-RDMFT response equations and various adiabatic approximations. None of the adiabatic approximations is fully satisfactory, so we also discuss a phase-dependent extension to TD-RDMFT employing the concept of phase-including-natural-spinorbitals (PINOs). We focus on applications of the linear response formulations to two-electron systems, for which the (almost) exact functional is known.
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open shell reduced Density Matrix functional theory
Journal of Chemical Physics, 2011Co-Authors: Daniel R Rohr, Katarzyna PernalAbstract:Open-shell reduced Density Matrix functional theory is established by investigating the domain of the exact functional. For spin states that are the ground state, a particularly simple set is found to be the domain. It cannot be generalized to other spin states. A number of conditions satisfied by the exact Density Matrix functional is formulated and tested for approximate functionals. The exact functional does not suffer from fractional spin error, which is the source of the static correlation error in dissociated molecules. We prove that a simple approximation (called the Buijse-Baerends functional, Muller or square root functional) has a non-positive fractional spin error. In the case of the H atom the error is zero. Numerical results for a few atoms are given for approximate Density and Density Matrix functionals as well as a recently developed range-separated combination of both.
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combining Density functional theory and Density Matrix functional theory
Physical Review A, 2010Co-Authors: Daniel R Rohr, Julien Toulouse, Katarzyna PernalAbstract:We combine Density-functional theory with Density-Matrix-functional theory to draw the best from both worlds. This is achieved by range separation of the electronic interaction which permits one to rigorously combine a short-range Density functional with a long-range Density-Matrix functional. The short-range Density functional is approximated by the short-range version of the Perdew-Burke-Ernzerhof functional (srPBE). The long-range Density-Matrix functional is approximated by the long-range version of the Buijse-Baerends functional (lrBB). The obtained srPBE+lrBB method accurately describes both the static and dynamic electron correlation at a computational cost similar to that of standard Density-functional approximations. This is shown for the dissociation curves of the H{sub 2}, LiH, BH, and HF molecules.
Garnet Kinlic Chan - One of the best experts on this subject based on the ideXlab platform.
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projected Density Matrix embedding theory with applications to the two dimensional hubbard model
arXiv: Chemical Physics, 2019Co-Authors: Zhihao Cui, Garnet Kinlic Chan, Yu Tong, Michael A Lindsey, Lin LinAbstract:Density Matrix embedding theory (DMET) is a quantum embedding theory for strongly correlated systems. From a computational perspective, one bottleneck in DMET is the optimization of the correlation potential to achieve self-consistency, especially for heterogeneous systems of large size. We propose a new method, called projected Density Matrix embedding theory (p-DMET), which achieves self-consistency without needing to optimize a correlation potential. We demonstrate the performance of p-DMET on the two-dimensional Hubbard model.
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the ab initio Density Matrix renormalization group in practice
Journal of Chemical Physics, 2015Co-Authors: Roberto Olivaresamaya, Sandeep Sharma, Naoki Nakatani, Jun Yang, Garnet Kinlic ChanAbstract:The ab-initio Density Matrix renormalization group (DMRG) is a tool that can be applied to a wide variety of interesting problems in quantum chemistry. Here, we examine the Density Matrix renormalization group from the vantage point of the quantum chemistry user. What kinds of problems is the DMRG well-suited to? What are the largest systems that can be treated at practical cost? What sort of accuracies can be obtained, and how do we reason about the computational difficulty in different molecules? By examining a diverse benchmark set of molecules: π-electron systems, benchmark main-group and transition metal dimers, and the Mn-oxo-salen and Fe-porphine organometallic compounds, we provide some answers to these questions, and show how the Density Matrix renormalization group is used in practice.
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the Density Matrix renormalization group in quantum chemistry
Annual Review of Physical Chemistry, 2011Co-Authors: Garnet Kinlic Chan, Sandeep SharmaAbstract:The Density Matrix renormalization group is a method that is useful for describing molecules that have strongly correlated electrons. Here we provide a pedagogical overview of the basic challenges of strong correlation, how the Density Matrix renormalization group works, a survey of its existing applications to molecular problems, and some thoughts on the future of the method.
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analytic response theory for the Density Matrix renormalization group
Journal of Chemical Physics, 2009Co-Authors: Jonathan J Dorando, Johannes Hachmann, Garnet Kinlic ChanAbstract:We propose an analytic response theory for the Density Matrix renormalization group, whereby response properties correspond to analytic derivatives of Density Matrix renormalization group observables with respect to the applied perturbations. Both static and frequency-dependent response theories are formulated and implemented. We evaluate our pilot implementation by calculating static and frequency-dependent polarizabilities of short oligodiacetylenes. The analytic response theory is competitive with dynamical Density Matrix renormalization group methods and yields significantly improved accuracies when using a small number of Density Matrix renormalization group states. Strengths and weaknesses of the analytic approach are discussed.
Iris Theophilou - One of the best experts on this subject based on the ideXlab platform.
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approximations based on Density Matrix embedding theory for Density functional theories
Electronic Structure, 2021Co-Authors: Iris Theophilou, Angel Rubio, Teresa E Reinhard, Michael RuggenthalerAbstract:Recently a novel approach to find approximate exchange-correlation functionals in Density-functional theory was presented (U. Mordovina et. al., JCTC 15, 5209 (2019)), which relies on approximations to the interacting wave function using Density-Matrix embedding theory (DMET). This approximate interacting wave function is constructed by using a projection determined by an iterative procedure that makes parts of the reduced Density Matrix of an auxiliary system the same as the approximate interacting Density Matrix. If only the diagonal of both systems are connected this leads to an approximation of the interacting-to-non-interacting mapping of the Kohn-Sham approach to Density-functional theory. Yet other choices are possible and allow to connect DMET with other Density-functional theories such as kinetic-energy Density functional theory or reduced Density-Matrix functional theory. In this work we give a detailed review of the basics of the DMET procedure from a Density-functional perspective and show how both approaches can be used to supplement each other. We do so explicitly for the case of a one-dimensional lattice system, as this is the simplest setting where we can apply DMET and the one that was originally presented. Among others we highlight how the mappings of Density-functional theories can be used to identify uniquely defined auxiliary systems and auxiliary projections in DMET and how to construct approximations for different Density-functional theories using DMET inspired projections. Such alternative approximation strategies become especially important for Density-functional theories that are based on non-linearly coupled observables such as kinetic-energy Density-functional theory, where the Kohn-Sham fields are no longer simply obtainable by functional differentiation of an energy expression, or for reduced Density-Matrix functional theories, where a straightforward Kohn-Sham construction is not feasible.
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approximations based on Density Matrix embedding theory for Density functional theories
arXiv: Chemical Physics, 2021Co-Authors: Iris Theophilou, Angel Rubio, Teresa E Reinhard, Michael RuggenthalerAbstract:Recently a novel approach to find approximate exchange-correlation functionals in Density-functional theory (DFT) was presented (U. Mordovina et. al., JCTC 15, 5209 (2019)), which relies on approximations to the interacting wave function using Density-Matrix embedding theory (DMET). This approximate interacting wave function is constructed by using a projection determined by an iterative procedure that makes parts of the reduced Density Matrix of an auxiliary system the same as the approximate interacting Density Matrix. If only the diagonal of both systems are connected this leads to an approximation of the interacting-to-non-interacting mapping of the Kohn-Sham approach to DFT. Yet other choices are possible and allow to connect DMET with other DFTs such as kinetic-energy DFT or reduced Density-Matrix functional theory. In this work we give a detailed review of the basics of the DMET procedure from a DFT perspective and show how both approaches can be used to supplement each other. We do so explicitly for the case of a one-dimensional lattice system, as this is the simplest setting where we can apply DMET and the one that was originally presented. Among others we highlight how the mappings of DFTs can be used to identify uniquely defined auxiliary systems and auxiliary projections in DMET and how to construct approximations for different DFTs using DMET inspired projections. Such alternative approximation strategies become especially important for DFTs that are based on non-linearly coupled observables such as kinetic-energy DFT, where the Kohn-Sham fields are no longer simply obtainable by functional differentiation of an energy expression, or for reduced Density-Matrix functional theories, where a straightforward Kohn-Sham construction is not feasible.
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reduced Density Matrix approach to strong matter photon interaction
ACS Photonics, 2019Co-Authors: Florian Buchholz, Iris Theophilou, S E B Nielsen, Michael Ruggenthaler, Angel RubioAbstract:We present a first-principles approach to electronic many-body systems strongly coupled to cavity modes in terms of matter-photon one-body reduced Density matrices. The theory is fundamentally non-perturbative and thus captures not only the effects of correlated electronic systems but accounts also for strong interactions between matter and photon degrees of freedom. We do so by introducing a higher-dimensional auxiliary system that maps the coupled fermion-boson system to a dressed fermionic problem. This reformulation allows us to overcome many fundamental challenges of Density-Matrix theory in the context of coupled fermion-boson systems and we can employ conventional reduced Density-Matrix functional theory developed for purely fermionic systems. We provide results for one-dimensional model systems in real space and show that simple Density-Matrix approximations are accurate from the weak to the deep-strong coupling regime.
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reduced Density Matrix approach to strong matter photon interaction
ACS Photonics, 2019Co-Authors: Florian Buchholz, Iris Theophilou, S E B Nielsen, Michael Ruggenthaler, Angel RubioAbstract:We present a first-principles approach to electronic many-body systems strongly coupled to cavity modes in terms of matter-photon one-body reduced Density matrices. The theory is fundamentally nonperturbative and thus captures not only the effects of correlated electronic systems but accounts also for strong interactions between matter and photon degrees of freedom. We do so by introducing a higher-dimensional auxiliary system that maps the coupled fermion-boson system to a dressed fermionic problem. This reformulation allows us to overcome many fundamental challenges of Density-Matrix theory in the context of coupled fermion-boson systems and we can employ conventional reduced Density-Matrix functional theory developed for purely fermionic systems. We provide results for one-dimensional model systems in real space and show that simple Density-Matrix approximations are accurate from the weak to the deep-strong coupling regime. This justifies the application of our method to systems that are too complex for exact calculations and we present first results, which show that the influence of the photon field depends sensitively on the details of the electronic structure.
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Generalized Pauli constraints in reduced Density Matrix functional theory
The Journal of Chemical Physics, 2015Co-Authors: Iris Theophilou, Miguel A. L. Marques, Nektarios N. Lathiotakis, N. HelbigAbstract:Functionals of the one-body reduced Density Matrix (1-RDM) are routinely minimized under Coleman’s ensemble N-representability conditions. Recently, the topic of pure-state N-representability conditions, also known as generalized Pauli constraints, received increased attention following the discovery of a systematic way to derive them for any number of electrons and any finite dimensionality of the Hilbert space. The target of this work is to assess the potential impact of the enforcement of the pure-state conditions on the results of reduced Density-Matrix functional theory calculations. In particular, we examine whether the standard minimization of typical 1-RDM functionals under the ensemble N-representability conditions violates the pure-state conditions for prototype 3-electron systems. We also enforce the pure-state conditions, in addition to the ensemble ones, for the same systems and functionals and compare the correlation energies and optimal occupation numbers with those obtained by the enforcement of the ensemble conditions alone.
