356 research outputs found
Spectral functions of the uniform electron gas via coupled-cluster theory and comparison to GW and related approximations
No full textWe use, for the first time, ab initio coupled-cluster theory to compute the spectral function of the uniform
electron gas at a Wigner-Seitz radius of rs = 4. The coupled-cluster approximations we employ go significantly
beyond the diagrammatic content of state-of-the-art GW theory. We compare our calculations extensively to
GW and GW-plus-cumulant theory, illustrating the strengths and weaknesses of these methods in capturing the
quasiparticle and satellite features of the electron gas. Our accurate calculations further allow us to address
the long-standing debate over the occupied bandwidth of metallic sodium. Our findings indicate that the future
application of coupled-cluster theory to condensed phase material spectra is highly promising
Judicial deference at work: Some reflections on Chan Kin Sum and Kong Yun Ming
No full text"Due deference" - the giving of appropriate weight to the government's judgment in the court's reasoning - is a tool that courts use to maintain the separation of powers in constitutional rights review. This note aims to provide a theoretical framework for understanding the issue of deference, and to analyse the Court of First Instance (CFI)'s approach to deference in two recent cases, Chan Kin Sum and Kong Yun Ming. The author argues that the CFI has adopted a spatial approach that failed to specify the contested issues that called for deference, inappropriately considered democratic legitimacy as a factor for deference and made broad presumptions about the democratic character of primary decisions. This approach may lead to an over-deferential attitude that threatens the separation of powers, and the malleability of the approach may be subject to courts' manipulation. The author argues for a more context-sensitive approach based purely on institutional factors.published_or_final_versio
Canonical transformation theory from extended normal ordering
No full textThe canonical transformation theory of Yanai and Chan [J. Chem. Phys. 124, 194106 (2006)] provides a rigorously size-extensive description of dynamical correlation in multireference problems. Here we describe a new formulation of the theory based on the extended normal ordering procedure of Mukherjee and Kutzelnigg [J. Chem. Phys. 107, 432 (1997)]. On studies of the water, nitrogen, and iron oxide potential energy curves, the linearized canonical transformation singles and doubles theory is competitive in accuracy with some of the best multireference methods, such as the multireference averaged coupled pair functional, while computational timings (in the case of the iron oxide molecule) are two to three orders of magnitude faster and comparable to those of the complete active space second-order perturbation theory. The results presented here are greatly improved both in accuracy and in cost over our earlier study as the result of a new numerical algorithm for solving the amplitude equations
An algorithm for large scale density matrix renormalization group calculations
No full textWe 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
No full textWe 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
No full textWe 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
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