Tensor product expansions for correlation in quantum many-body systems

Gabor Csanyi; T. A. Arias

Home/Archive/arXiv

arXiv · cond-mat/9805388

Tensor product expansions for correlation in quantum many-body systems

Gabor Csanyi·T. A. Arias

View original source ↗Read source document ↗Export metadata ↓

Abstract

We explore a new class of computationally feasible approximations of the two-body density matrix as a finite sum of tensor products of single-particle operators. Physical symmetries then uniquely determine the two-body matrix in terms of the one-body matrix. Representing dynamical correlation alone as a single tensor product results in a theory which predicts near zero dynamical correlation in the homogeneous electron gas at moderate to high densities. But, representing both dynamical and statistical correlation effects together as a tensor product leads to the recently proposed ``natural orbital functional.'' We find that this latter theory has some asymptotic properties consistent with established many-body theory but is no more accurate than Hartee-Fock in describing the homogeneous electron gas for the range of densities typically found in the valence regions of solids. PACS 71.10.-w 71.15.Mb, Accepted for publication in Physical Review B

Explore related subjects

cond-mat.mtrl-sci cond-mat.str-el

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Gabor Csanyi, T. A. Arias. 1999-11-14. Tensor product expansions for correlation in quantum many-body systems. https://arxiv.org/abs/cond-mat/9805388

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Electronic States, Spin-Orbit Coupling and Magnetism in Germanium 60° Dislocations

Defects in semiconductors have recently attracted renewed interest owing to their potential in novel quantum applications. Here we investigate the electronic and magnetic properties induced by 60° dislocations in Ge. Using large-scale DFT calculations, we determine the band structure for both the shuffle and glide sets in their lowest-energy configurations. The band structure for the shuffle set reveals defect-induced dispersive bands localized within the band gap near the $Γ$ point, whereas for the glide set, we observe strong overlap with the conduction band. Defect-induced band splitting evident away from $Γ$ reveals Rashba-Dresselhaus spin-orbit coupling, an effect previously reported only for screw dislocations. Remarkably, we find evidence that specific dislocation arrangements can stabilize antiferromagnetic ordering with sizable local magnetic moments and considerable exchange splitting between opposite spin states. These results uncover rich physics in Ge dislocations through the combination of spin-orbit coupling and magnetic ordering, potentially enabling novel defect-based functionalities in Ge devices.

cond-mat.mtrl-sci↗

arXiv2026

Thermal Hall resistivity and transverse entropy production in a phonon gas

Most theories of the phonon thermal Hall effect ignore phonon-phonon interactions. Here, by recalling the Senftleben-Beenakker effect in molecular gases, we argue that a magnetic field, by influencing collisions between neutral non-chiral [quasi-]particles, can induce a Hall response. Our study of two insulators with distinct crystal structures, layered honeycomb WS$_2$ and ferroelectric perovskite LiNbO$_3$, finds that $κ_{xx}$ and $κ_{xy}$ peak at nearly the same temperature in both materials, as reported in other insulators. We show that the amplitude of transverse thermal \emph{resistivity} in clean and simple insulators is of the order of $|W_\perp/B|\simeq \frac{e}{k_B u}$, where $e$ and $k_B$ are fundamental constants and $u$ is the binding energy density of the crystal. In complex and dirty insulators, $|W_\perp/B|$ is much larger and has a significant temperature dependence. Nevertheless, the peak thermal Hall \textit{angle} in all insulators remains roughly the same.

cond-mat.mtrl-sci↗

arXiv2026

First-principles calculations of electronic structure

The emergence of high-mobility at provides a fertile platform for exploring emergent quantum phenomena and next-generation oxide electronics. Here, using first-principles density functional theory (DFT) calculations, we uncover the microscopic origin of the formed at the interface between insulators. Despite both constituents being insulating in bulk, the heterostructure develops robust metallicity at the interface, in agreement with experimental observations. This charge redistribution stabilizes at the interface. The electronic states forming enforcing carrier motion strictly within the interfacial plane. Remarkably, the spin-up parabolic band hosting the 2DEG exhibits an exceptionally small effective mass -- indicating the potential for significantly enhanced carrier mobility. Furthermore, the calculated interfacial electron density exceeds that of by nearly an order of magnitude, consistent with experimental measurement. These findings identify the heterostructure as a compelling platform for realizing and open new avenues for engineering correlated oxide interfaces for quantum electronic applications.

cond-mat.mtrl-sci↗