Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “density matrix renormalization”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 253 records · Page 14
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Origin of Insulating Ferromagnetism in Iron Oxychalcogenide Ce 2 O 2 FeSe 2

An insulating ferromagnetic (FM) phase exists in the quasi-one-dimensional iron oxychalcogenide Ce 2 O 2 FeSe 2 , but its origin is unknown. To understand the FM mechanism, here a systematic investigation of this material is provided, analyzing the competition between ferromagnetic and antiferromagnetic tendencies and the interplay of hoppings, Coulomb interactions, Hund’s coupling, and crystal-field splittings. Overall, our intuitive analysis based on second-order perturbation theory shows that large entanglements between doubly occupied and half filled orbitals play a key role in stabilizing the FM order in Ce 2 O 2 FeSe 2 . In addition, via many-body computational techniques applied to a multiorbital Hubbard model, the phase diagram confirms the proposed FM mechanism.

1-dimensional spin chains↗
DOE OSTI2023

Witnessing Nonequilibrium Entanglement Dynamics in a Strongly Correlated Fermionic Chain

Many-body entanglement in condensed matter systems can be diagnosed from equilibrium response functions through the use of entanglement witnesses and operator-specific quantum bounds. Here, we investigate the applicability of this approach for detecting entangled states in quantum systems driven out of equilibrium. We use a multipartite entanglement witness, the quantum Fisher information, to study the dynamics of a paradigmatic fermion chain undergoing a time-dependent change of the Coulomb interaction. Our results show that the quantum Fisher information is able to witness distinct signatures of multipartite entanglement both near and far from equilibrium that are robust against decoherence. Here, we discuss implications of these findings for probing entanglement in light-driven quantum materials with time-resolved optical and x-ray scattering methods.

1-dimensional spin chains↗
DOE OSTI2024

Extracting Higher Central Charge from a Single Wave Function

A (2+1)D topologically ordered phase may or may not have a gappable edge, even if its chiral central charge c_ is vanishing. Recently, it was discovered that a quantity regarded as a "higher" version of chiral central charge gives a further obstruction beyond c_ to gapping out the edge. Here, in this Letter, we show that the higher central charges can be characterized by the expectation value of the partial rotation operator acting on the wave function of the topologically ordered state. This allows us to extract the higher central charge from a single wave function, which can be evaluated on a quantum computer. Our characterization of the higher central charge is analytically derived from the modular properties of edge conformal field theory, as well as the numerical results with the ν = 1/2 bosonic Laughlin state and the non-Abelian gapped phase of the Kitaev honeycomb model, which corresponds to U(1) 2 and Ising topological order, respectively. The Letter establishes a numerical method to obtain a set of obstructions to the gappable edge of (2+1)D bosonic topological order beyond c_, which enables us to completely determine if a (2+1)D bosonic Abelian topological order has a gappable edge or not. We also point out that the expectation values of the partial rotation on a single wave function put a constraint on the low-energy spectrum of the bulk-boundary system of (2+1)D bosonic topological order, reminiscent of the Lieb-Schultz-Mattis-type theorems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Higher Hall conductivity from a single wave function: Obstructions to symmetry-preserving gapped edge of (2+1)-dimensional topological order

A (2+1)D topologically ordered phase with U(1) symmetry may or may not have a symmetric gapped edge state, even if both thermal and electric Hall conductivity are vanishing. It has recently been discovered that there are “higher” versions of Hall conductivity valid for fermionic fractional quantum Hall (FQH) states that obstruct symmetry-preserving gapped edge states beyond thermal and electric Hall conductivity. In this paper, we show that one can extract higher Hall conductivity from a single wave function of an FQH state, by evaluating the expectation value of the “partial rotation” unitary, which is a combination of partial spatial rotation and a U(1) phase rotation. This result is verified numerically with the fermionic Laughlin state with 𝜈=1/3 and 1/5, as well as the non-Abelian Moore-Read state. Together with topological entanglement entropy, we prove that the expectation values of the partial rotation completely determine if a bosonic/fermionic Abelian topological order with U(1) symmetry has a symmetry-preserving gappable edge state or not. We also show that thermal and electric Hall conductivity of Abelian topological order can be extracted by partial rotations. Even in non-Abelian FQH states, partial rotation provides the Lieb-Schultz-Mattis type theorem constraining the low-energy spectrum of the bulk-boundary system. The generalization of higher Hall conductivity to the case with Lie group symmetry is also presented.

2-dimensional systems↗
DOE OSTI2020

Off-shell effective energy theory: A unified treatment of the Hubbard model from $\textit{d} = 1$ to $\textit{d = ∞}$

Here we propose an exact formalism, off-shell effective energy theory (OET), which provides a thermodynamic description of a generic quantum Hamiltonian. The OET is based on a partitioning of the Hamiltonian and a corresponding density matrix ansatz constructed from an off-shell extension of the equilibrium density matrix; and there are dual realizations based on a given partitioning. To approximate OET, we introduce the central point expansion (CPE), which is an expansion of the density matrix ansatz, and we renormalize the CPE using a standard expansion of the ground-state energy. In this work we showcase the OET for the one-band Hubbard model in $\textit{d}$ = 1 , 2, and $\infty$, using a partitioning between kinetic and potential energy, yielding two realizations denoted as $\mathcal{K}$ and $\mathcal{X}$. OET shows favorable agreement with exact or state-of-the-art results over all parameter space, and has a negligible computational cost. Physically, $\mathcal{K}$ describes the Fermi liquid, while $\mathcal{X}$ gives an analogous description of both the Luttinger liquid and the Mott insulator. Our approach should find broad applicability in lattice model Hamiltonians, in addition to real materials systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Electronic Structure Theory and Novel Materials

This grant supported research on electronic structure and materials theory, with focus on three main issues: (i) novel techniques to deal with correlation in the electronic ground-state, (ii) topological materials, (iii) the phase diagram of lattice spin models. Regarding (i), we applied to the homogeneous electron liquid an approach that we previously developed in the context of molecular systems. In this scheme the electronic occupation probabilities and the natural spin orbitals are used to construct an approximate two-body density matrix for the electronic ground-state. Regarding (ii) we used standard electronic structure methods based on density functional theory to model topological materials and interpret experimental observations. Finally, regarding (iii) we further developed a numerical approach to compute the renormalized couplings within real space renormalization group theory in the context of lattice spin models. The main findings were the following. (i) We found that with our approximate two-body density matrix, which works well for small molecules, is not sufficiently accurate for condensed phase systems. Missing a systematic way of improving on the adopted approximations, we decided not to pursue this approach. (ii) We performed two studies. In one, we investigated the influence of Te defects on the topological properties of a WTe2 monolayer, finding that while Te vacancies, even in modest concentration, destroy the topological character, Te adatoms do not, consistent with a recent experiment. In another study, we predicted Weyl semimetal character and strong anomalous Hall effect in the Heusler compensated ferrimagnet Ti2MnAl. (iii) We developed a new Monte Carlo method to do real space renormalization group calculations for lattice spin models. We subsequently extended the scheme to deal with lattice spin models in presence of quenched disorder, finding that the approach can distinguish systems with finite and strong disorder. In the finite disorder case, the method allows one to find with good approximation the critical coupling distribution and the critical exponents.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Exact two-body expansion of the many-particle wave function

Progress toward the solution of the strongly correlated electron problem has been stymied by the exponential complexity of the wave function. Previous work established an exact two-body exponential product expansion for the ground-state wave function. By developing a reduced density-matrix analog of Dalgarno-Lewis perturbation theory, we prove here that (i) the two-body exponential product expansion is rapidly and globally convergent with each operator representing an order of a renormalized perturbation theory, (ii) the energy of the expansion converges quadratically near the solution, and (iii) the expansion is exact for both ground and excited states. The two-body expansion offers a reduced parametrization of the many-particle wave function as well as the two-particle reduced density matrix with potential applications on both conventional and quantum computers for the study of strongly correlated quantum systems. In this work, we demonstrate the result with the exact solution of the contracted Schrödinger equation for the molecular chains H 4 and H 5 .

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Sub-system self-consistency in coupled cluster theory

Here, in this article, we provide numerical evidence indicating that the single-reference coupled-cluster (CC) energies can be calculated alternatively to their copybook definition. We demonstrate that the CC energy can be reconstructed by diagonalizing the effective Hamiltonians describing correlated sub-systems of the many-body system. In the extreme case, we provide numerical evidence that the CC energy can be reproduced through the diagonalization of the effective Hamiltonian describing sub-system composed of a single electron. These properties of the CC formalism can be exploited to design protocols to define effective interactions in sub-systems used as probes to calculate the energy of the entire system and introduce a new type of self-consistency for approximate CC approaches.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Pressure-induced 𝐵⁢1 to 𝐵⁢2 phase transition in CeN studied by 𝑎⁢𝑏 𝑖⁢𝑛⁢𝑖⁢𝑡⁢𝑖⁢𝑜 correlation matrix renormalization theory calculations

We apply correlation matrix renormalization theory (CMRT) to cerium nitride (CeN) under pressure. For 𝐵⁢1 (NaCl-type) phase, CMRT gives an equation of state consistent with ambient pressure experiments. It produces electronic density-of-state (DOS) characterized by a sharp 4⁢𝑓 quasiparticle resonance peak pinned at the Fermi level and two subbands formed by strong hybridization between the localized Ce-4⁢𝑓 electrons and the itinerant Ce-5⁢𝑑 and N-2⁢𝑝 electrons below the Fermi level, consistent with x-ray photoemission spectroscopy experiments. Upon compression, CMRT predicts a first-order 𝐵⁢1 → 𝐵⁢2 (CsCl-type) transition with ∼11% volume collapse in agreement with experiments. Across the transition, the 4⁢𝑓 spectrum broadens, the 4⁢𝑓 orbital occupancy increases, and the hybridization with conduction states enhances, signaling a crossover from partially localized to more itinerant 4⁢𝑓 behavior. Furthermore, these features are in excellent agreement with experimental observations, demonstrating that CMRT provides a parameter-free description and prediction of correlation-driven structural and electronic transitions in rare-earth compounds.

Ab initio calculations↗
DOE OSTI2021

Quantum many-body simulations of the two-dimensional Fermi-Hubbard model in ultracold optical lattices

Understanding quantum many-body states of correlated electrons is one main theme in modern condensed-matter physics. Given that the Fermi-Hubbard model, the prototype of correlated electrons, was recently realized in ultracold optical lattices, it is highly desirable to have controlled numerical methodology to provide precise finite-temperature results upon doping to directly compare with experiments. Here, we demonstrate the exponential tensor renormalization group (XTRG) algorithm [Chen et al., Phys. Rev. X 8, 031082 (2018)], complemented by independent determinant quantum Monte Carlo, offers a powerful combination of tools for this purpose. XTRG provides full and accurate access to the density matrix and thus various spin and charge correlations, down to an unprecedented low temperature of a few percent of the tunneling energy. Finally, we observe excellent agreement with ultracold fermion measurements at both half filling and finite doping, including the sign-reversal behavior in spin correlations due to formation of magnetic polarons, and the attractive hole-doublon and repulsive hole-hole pairs that are responsible for the peculiar bunching and antibunching behaviors of the antimoments.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Layer-dependent spin-resolved electronic structure of ferromagnetic triple-layered ruthenate Sr4Ru3O10

High-resolution angle- and spin-resolved photoemission spectroscopy (ARPES) of the triple-layered ruthenate Sr4Ru3O10 reveals features of the electronic structure that extend our understanding of the layered strontium ruthenates. The spectra near the Fermi energy are very different from the nonmagnetic analogues Sr2RuO4 and Sr3Ru2O7 with distinct Fermi surfaces for wide electronlike minority spin bands around the zone center and narrow holelike majority spin Fermi surface contours around the zone corners. The most dramatic results are two narrow spectral peaks ∼30 meV below the Fermi level, a spin-minority holelike band at the Brillouin zone center, and a spin-majority saddle-band van Hove singularity at the zone edge, which exhibits almost 100% spin polarization at low temperature, and a strong temperature dependent coherence-incoherence crossover attributed to Hund metal correlations. Quantitative comparison of the ARPES to spin-polarized density functional theory (DFT) calculations identify the specific antibonding and nonbonding orbital origins of the narrow bands, with a prediction of different spatial localization in the central and outer layers. This is shown to be consistent with experimental ARPES multizone matrix element intensity variations, and implicates outer-layer-specific control of the in-plane metamagnetism. The renormalization of the bands relative to the mean-field DFT, the demonstration of spin-polarized oxygen bands, and of spin-minority and spin-majority band-crossing hybridization provide a more complete picture of the magnetism which displays aspects of both delocalized and local moment behavior.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Photoinduced anomalous Hall effect in two-dimensional transition metal dichalcogenides

A circularly polarized ac pump field illuminated near resonance on two-dimensional transition metal dichalcogenides (TMDs) produces an anomalous Hall effect in response to a dc bias field. In this work, we develop a theory for this photoinduced anomalous Hall effect in undoped TMDs irradiated by a strong coherent laser field. The strong field renormalizes the equilibrium bands and opens up a dynamical energy gap where single-photon resonance occurs. The resulting photon dressed states, or Floquet states, are treated within the rotating-wave approximation. A quantum kinetic equation approach is developed to study the nonequilibrium density matrix and time-averaged transport currents under the simultaneous influence of the strong ac pump field and the weak dc probe field. Dissipative effects are taken into account in the kinetic equation that captures relaxation and dephasing. The photoinduced longitudinal and Hall conductivities display notable resonant signatures when the pump field frequency reaches the spin-split interband transition energies. Rather than valley polarization, we find that the anomalous Hall current is mainly driven by the intraband response of photon-dressed electron populations near the dynamical gap at both valleys, accompanied by a smaller contribution due to the interband response. In conclusion, these findings highlight the importance of photon-dressed bands and nonequilibrium distribution functions in achieving a proper understanding of the photoinduced anomalous Hall effect in a strong pump field.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Unified ab initio description of Fröhlich electron-phonon interactions in two-dimensional and three-dimensional materials

Ab initio calculations of electron-phonon interactions including the polar Fröhlich coupling have advanced considerably in recent years. The Fröhlich electron-phonon matrix element is by now well understood in the case of bulk three-dimensional (3D) materials. In the case of two-dimensional (2D) materials, the standard procedure to include Fröhlich coupling is to employ Coulomb truncation, so as to eliminate artificial interactions between periodic images of the 2D layer. While these techniques are well established, the transition of the Fröhlich coupling from three to two dimensions has not been investigated. Furthermore, it remains unclear what error one makes when describing 2D systems using the standard bulk formalism in a periodic supercell geometry. In this work, we generalize previous work on the ab initio Fröhlich electron-phonon matrix element in bulk materials by investigating the electrostatic potential of atomic dipoles in a periodic supercell consisting of a 2D material and a continuum dielectric slab. We obtain a unified expression for the matrix element, which reduces to the existing formulas for three-dimensional and 2D systems when the interlayer separation tends to zero or infinity, respectively. This expression enables an accurate description of the Fröhlich matrix element in 2D systems without resorting to Coulomb truncation. We validate our approach by direct ab initio density-functional perturbation theory calculations for monolayer BN and MoS 2 , and we provide a simple expression for the 2D Fröhlich matrix element that can be used in model Hamiltonian approaches. The formalism outlined in this work may find applications in calculations of polarons, quasiparticle renormalization, transport coefficients, and superconductivity, in 2D and quasi-2D materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗