1,721,137 research outputs found
An algorithm for large scale density matrix renormalization group calculations
Full text linkWe describe in detail our high-performance density matrix renormalization group (DMRG) algorithm for solving the electronic Schrödinger equation. We illustrate the linear scalability of our algorithm with calculations on up to 64 processors. The use of massively parallel machines in conjunction with our algorithm considerably extends the range of applicability of the DMRG in quantum chemistry
Quantum algorithms of interest on NISQ machines
No full textI will explore a few possibilities for quantum algorithms and quantum simulations of interest on NISQ machines
Low entanglement wavefunctions
No full textWe review a class of efficient wavefunction approximations that are based around the limit of low entanglement. These wavefunctions, which go by such names as matrix product states and tensor network states, occupy a different region of Hilbert space from wavefunctions built around the Hartree–Fock limit. The best known class of low entanglement wavefunctions, the matrix product states, forms the variational space of the density matrix renormalization group algorithm. Because of their different structure to many other quantum chemistry wavefunctions, low entanglement approximations hold promise for problems conventionally considered hard in quantum chemistry, and in particular problems which have a multireference or strong correlation nature. In this review, we describe low entanglement wavefunctions at an introductory level, focusing on the main theoretical ideas. Topics covered include the theory of efficient wavefunction approximations, entanglement, matrix product states, and tensor network states including the tree tensor network, projected entangled pair states, and the multiscale entanglement renormalization ansatz
Density Matrix Renormalization Group Lagrangians
Full text linkWe introduce a Lagrangian formulation of the Density Matrix Renormalization Group (DMRG). We present Lagrangians which when minimised yield the optimal DMRG wavefunction in a variational sense, both within the general matrix product ansatz, as well as within the canonical form of the matrix product that is constructed within the DMRG sweep algorithm. Some of the results obtained are similar to elementary expressions in Hartree-Fock theory, and we draw attention to such analogies. The Lagrangians introduced here will be useful in developing theories of analytic response and derivatives in the DMRG
Quantum chemistry, classical heuristics, and quantum advantage
Full text linkWe describe the problems of quantum chemistry, the intuition behind classical heuristic methods used to solve them, a conjectured form of the classical complexity of quantum chemistry problems, and the subsequent opportunities for quantum advantage. This article is written for both quantum chemists and quantum information theorists. In particular, we attempt to summarize the domain of quantum chemistry problems as well as the chemical intuition that is applied to solve them within concrete statements (such as a classical heuristic cost conjecture and a classification of different avenues for quantum advantage) in the hope that this may stimulate future analysis
Coupled cluster methods in condensed phase chemistry
No full textI will describe recent developments in coupled cluster methods in condensed phase systems, including (i) finite temps. (ii) electron-phonon coupling, and (iii) methods for spectra
Density matrix renormalisation group Lagrangians
Full text linkWe introduce a Lagrangian formulation of the density matrix renormalisation group (DMRG). We present Lagrangians which, when minimised, yield the optimal DMRG wavefunction in a variational sense, both within the general matrix product ansatz and within the canonical form of the matrix product that is constructed within the DMRG sweep algorithm. Some of the results obtained are similar to elementary expressions in Hartree–Fock theory, and we draw attention to such analogies. The Lagrangians introduced here will be useful in developing theories of analytic response and derivatives in the DMRG
A fresh look at ensembles: Derivative discontinuities in density functional theory
Full text linkWe present a zero temperature ensemble spin density functional theory. We discuss the ensemble quantities that arise from derivative discontinuities, including the nonvanishing asymptotic potential and band gap shift, in the context of the Kohn–Sham formalism, and hybrid exact exchange theories, such as the Hartree–Fock–Kohn–Sham formalism. We describe and implement a general method of calculating these quantities in atomic and molecular systems. Finally we discuss how our results explain the deficiencies of existing functionals, and how new functionals should be constructed, illustrating our conclusions by examining the dissociation of H^(+)_2
An extensive study of gradient approximations to the exchange-correlation and kinetic energy functionals
Full text linkWe formalize the procedure of functional development, in a general theoretical framework. Expansion in a functional basis set, and fitting via an error functional to a data set, casts functional development as a variational problem to obtain the functional basis-set and data-set limits. Overfitting is avoided by defining the optimum number of parameters. We implement our theory for an investigation of first- and second-order generalized gradient approximations (GGA) to the exchange-correlation and kinetic energy functionals, within an ab initio model. A variety of functional basis sets, including a general finite-element representation, is constructed to represent both one-dimensional and multidimensional GGA enhancement factors. An extensible data set consisting of 429 atomic and diatomic, neutral and cationic species, at stretched and equilibrium geometries, is constructed from Moller–Plesset level exchange-correlation energies, and Hartree–Fock kinetic energies. The range of chemically relevant density and gradient variables is examined. Exhaustive fitting investigations are carried out, to determine the accuracy of the GGA representation of the ab initio models. In the exchange-correlation case we demonstrate that we can reach the functional basis-set and data-set limit, which correspond to a root-mean-square (rms) error of ∼10∼10 mH (6.3 kcal/mol). Changing the functional basis set, higher-order density variables such as the kinetic energy density, multidimensional enhancement factors, and exact exchange yield no significant improvement, and our fits represent an effective solution of the GGA problem for exchange-correlation, at the Møller–Plesset level. In the kinetic energy case, accurate functionals with rms errors of ∼80∼80 mH (50 kcal/mol) are developed. These exhibit a beautifully simple kinetic energy enhancement factor, and are a step towards orbital-free calculations
First principles coupled cluster theory of the electronic spectrum of the transition metal dichalcogenides
Full text linkThe electronic properties of two-dimensional transition metal dichalcogenides (2D TMDs) have attracted much attention during the last decade. We show how a diagrammatic ab initio coupled cluster singles and doubles (CCSD) treatment paired with a careful thermodynamic limit extrapolation in two dimensions can be used to obtain converged band gaps for monolayer materials in the MoS₂ family. We find CCSD gaps to lie in the upper range of the spread of GW approximation based on density functional theory (DFT) simulations, and also find slightly higher effective hole masses compared to previous reports. We also investigate the ability of CCSD to describe trion states, finding a reasonable qualitative structure, but poor excitation energies due to the lack of screening of three-particle excitations in the effective Hamiltonian. Our study provides an independent high-level benchmark of the role of many-body effects in 2D TMDs and showcases the potential strengths and weaknesses of diagrammatic coupled cluster approaches for realistic materials
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