The tensor hypercontracted parametric reduced density matrix algorithm: coupled-cluster accuracy with O(r^4) scaling

Tensor hypercontraction is a method that allows the representation of a high-rank tensor as a product of lower-rank tensors. In this paper, we show how tensor hypercontraction can be applied to both the electron repulsion integral (ERI) tensor and the two-particle excitation amplitudes used in the parametric reduced density matrix (pRDM) algorithm. Because only O(r) auxiliary functions are needed in both of these approximations, our overall algorithm can be shown to scale as O(r4), where r is the number of single-particle basis functions. We apply our algorithm to several small molecules, hydrogen chains, and alkanes to demonstrate its low formal scaling and practical utility. Provided we use enough auxiliary functions, we obtain accuracy similar to that of the traditional pRDM algorithm, somewhere between that of CCSD and CCSD(T).Comment: 11 pages, 1 figur

The Ground State of the ``Frozen'' Electron Phase in Two-Dimensional Narrow-Band Conductors with a Long-Range Interelectron Repulsion. Stripe Formation and Effective Lowering of Dimension

In narrow-band conductors a weakly screened Coulomb interelectron repulsion can supress narrow-band electrons' hopping, resulting in formation of a ``frozen'' electron phase which differs principally from any known macroscopic self-localized electron state including the Wigner crystal. In a zero-bandwidth limit the ``frozen'' electron phase is a classical lattice system with a long-range interparticle repulsion. The ground state of such systems has been considered in the case of two dimensions for an isotropic pair potential of the mutual particle repulsion. It has been shown that particle ordering into stripes and effective lowering of dimension universally resides in the ground state for any physically reasonable pair potential and for any geometry of the conductor lattice. On the basis of this fact a rigorous general procedure to fully describe the ground state has been formulated. Arguments have been adduced that charge ordering in High-T_c superconductors testifies to presence of a ``frozen'' electron phase in these systems.Comment: 5 pages, LaTeX 2.09, 1 figure in external PostScript files. To appear in Phys.Rev B Rapid Communication

Neural Relax

We present an algorithm for data preprocessing of an associative memory inspired to an electrostatic problem that turns out to have intimate relations with information maximization

Cavity-mediated electron-photon superconductivity

We investigate electron paring in a two-dimensional electron system mediated by vacuum fluctuations inside a nanoplasmonic terahertz cavity. We show that the structured cavity vacuum can induce long-range attractive interactions between current fluctuations which lead to pairing in generic materials with critical temperatures in the low-Kelvin regime for realistic parameters. The induced state is a pair density wave superconductor which can show a transition from a fully gapped to a partially gapped phase - akin to the pseudogap phase in high-$T_c$ superconductors. Our findings provide a promising tool for engineering intrinsic electron interactions in two-dimensional materials.Comment: 11 page

The dynamics of highly excited electronic systems: Applications of the electron force field

Highly excited heterogeneous complex materials are essential elements of important processes, ranging from inertial confinement fusion to semiconductor device fabrication. Understanding the dynamics of these systems has been challenging because of the difficulty in extracting mechanistic information from either experiment or theory. We describe here the electron force field (eFF) approximation to quantum mechanics which provides a practical approach to simulating the dynamics of such systems. eFF includes all the normal electrostatic interactions between electrons and nuclei and the normal quantum mechanical description of kinetic energy for the electrons, but contains two severe approximations: first, the individual electrons are represented as floating Gaussian wave packets whose position and size respond instantaneously to various forces during the dynamics; and second, these wave packets are combined into a many-body wave function as a Hartree product without explicit antisymmetrization. The Pauli principle is accounted for by adding an extra spin-dependent term to the Hamiltonian. These approximations are a logical extension of existing approaches to simulate the dynamics of fermions, which we review. In this paper, we discuss the details of the equations of motion and potentials that form eFF, and evaluate the ability of eFF to describe ground-state systems containing covalent, ionic, multicenter, and/or metallic bonds. We also summarize two eFF calculations previously reported on electronically excited systems: (1) the thermodynamics of hydrogen compressed up to ten times liquid density and heated up to 200 000 K; and (2) the dynamics of Auger fragmentation in a diamond nanoparticle, where hundreds of electron volts of excitation energy are dissipated over tens of femtoseconds. These cases represent the first steps toward using eFF to model highly excited electronic processes in complex materials