SEARCH · Engineering Papers

Results for “density matrix”

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.

SourceResearch connectionFrom yearThrough year

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

At least 289 records · Page 16

All sources NASA NTRS DOE OSTI

DOE OSTI2025

Global phase diagram of D-wave superconductivity in the square-lattice t-J model

The Hubbard and closely related t-J models are exciting platforms for unconventional superconductivity (SC). Through state-of-the-art density matrix renormalization group calculations using the grand canonical ensemble, we address open issues regarding the ground-state phase diagram of the extended t-J model on a square lattice in the parameter regime relevant to cuprate superconductors. On large 8-leg cylinders, we demonstrate that the pure t-J model with only nearest-neighbor hoppings and superexchange interactions, for a wide range of doping ( δ = 0.1 to 0.2 ), hosts robust d-wave superconductivity possibly coexisting with weak unidirectional pair density wave. Furthermore, a small next nearest neighbor hopping t 2 suppresses pair and charge density waves, resulting in a uniform d-wave SC phase in both electron- and hole-doped cuprate model systems. Our work validates the t-J model as a proper minimum model for the emergence of superconductivity in cuprate superconductors.

Chen, Feng (ORCID:000000018196030X)↗

DOE OSTI2023

Plasmon-enhanced optical nonlinearity in graphene nanomeshes

Using the density-matrix formalism, here we show that graphene nanomeshes (GNMs)—graphene sheets patterned with antidots—have large plasmon-enhanced nonlinear optical response. GNMs can be designed to behave as quasi-one-dimensional plasmonic crystals in which plasmons with large propagation lengths are efficiently excited. The associated third-order Kerr and third-harmonic-generation susceptibility can be as high as 10 –7 and 10 –9 m 2 V –2 , respectively, over the mid-to-near-infrared frequency range. Furthermore, carrier-density tuning in GNMs can flip the propagation direction of plasmonic waves and enables bidirectional switching of optical signals.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2020

Dirty bosons on the Cayley tree: Bose-Einstein condensation versus ergodicity breaking

Building on large-scale quantum Monte Carlo simulations, we investigate the zero-temperature phase diagram of hard-core bosons in a random potential on site-centered Cayley trees with branching number K=2. In order to follow how the Bose-Einstein condensate (BEC) is affected by the disorder, we focus on both the zero-momentum density, probing the quantum coherence, and the one-body density matrix (1BDM) whose largest eigenvalue monitors the off-diagonal long-range order. We further study its associated eigenstate which brings useful information about the real-space properties of this leading eigenmode. Upon increasing randomness, we find that the system undergoes a quantum phase transition at finite disorder strength between a long-range ordered BEC state, fully ergodic at large scale, and a new disordered Bose glass regime showing conventional localization for the coherence fraction while the 1BDM displays a nontrivial algebraic vanishing BEC density together with a nonergodic occupation in real space. These peculiar properties can be analytically captured by a simple phenomenological description on the Cayley tree which provides a physical picture of the Bose glass regime.

36 MATERIALS SCIENCE↗

NASA NTRSDate not supplied

Use of Spectral Analysis of Singular Values as a Test Metric for IMMAT Trials

One of many challenges in the implementation of multiple exciter testing is establishing a reasonable set of test metrics to measure the quality of testing. This is especially true in the application of Impedance Matched Multi-Axis Testing; in that it is possible to have very large spectral density matrices that serve as reference criteria. While there exist plotting schemes to view a spectral density matrix, it is often necessary to break the overlay of reference and test results into subsections of the matrices to get sufficient resolution to interpret the data. In addition, as one attempts to control multiple locations on a structure, implementation of classical single degree-of freedom test tolerances across all channels and associated cross spectra is simply not feasible. Hence it is challenging to evaluate overall test quality. The use of spectral views of the dominant singular values from the singular value decomposition of the spectral density matrices and metrics based upon them is proposed for establishing a set of compact metrics for evaluating test quality. A laboratory experiment will be included to demonstrate this proposed technique.

Impedance Matched Multi-Axis Testing↗

NASA NTRSDate not supplied

Use of Spectral Analysis of Singular Values as a Test Metric for Impedance Matched Multi-Axis Test Trials

Vibration Testing↗

NASA NTRS2003

Collective Excitations in InAs Well Intersubband Transitions

Intersubband transitions in semiconductor quantum well are studied using a density matrix theory that goes beyond the Hartree-Fock approximation by including the full second order electron-electron scattering terms in the polarization equation for the first time. Even though the spectral features remain qualitatively similar to the results obtained with dephasing rate approximation, significant quantitative changes result from such a more detailed treatment of dephasing. More specifically, we show how the interplay of the two fundamental collective excitations, the Fermi-edge singularity and the intersubband plasmon, leads to significant changes in lineshape as the electron density varies.

Li, Jian-Zhong↗

DOE OSTI2020

Prediction of exotic magnetic states in the alkali-metal quasi-one-dimensional iron selenide compound Na 2 FeSe 2

The magnetic and electronic phase diagram of a model for the quasi-one-dimensional alkali-metal iron selenide compound Na 2 FeSe 2 is presented. The novelty of this material is that the valence of iron is Fe 2+ , contrary to most other iron-chain compounds with valence Fe 3+ . Using first-principles techniques, we developed a three-orbital tight-binding model that reproduces the ab initio band structure near the Fermi level. Including Hubbard and Hund couplings and studying the model via the density-matrix renormalization group and Lanczos methods, we constructed the ground-state phase diagram. A robust region where the block state ↑↑↓↓↑↑↓↓ is stabilized was unveiled. The analog state in iron ladders, employing 2×2 ferromagnetic blocks, is by now well established, but in chains a block magnetic order has not been observed yet in real materials. The phase diagram also contains a large region of canonical staggered spin order ↑↓↑↓↑↓↑ at very large Hubbard repulsion. At the block-to-staggered transition region, an exotic phase is stabilized with a mixture of both states: an inhomogeneous orbital-selective charge density wave with the exotic spin configuration ↑↑↓↑↓↓↑↓. Our predictions for Na 2 FeSe 2 may guide crystal growers and neutron-scattering experimentalists towards the realization of block states in one-dimensional iron selenide chain materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2024

Pairing tendencies in the doped Kitaev-Heisenberg model

Here, we study the impact of hole doping on the Kitaev-Heisenberg model on the honeycomb lattice. We investigate the pairing tendencies and correlation functions in the framework of a t - J - K model using density matrix renormalization group calculations on three-leg cylinders. In the case of the pure Kitaev model, which realizes a quantum spin-liquid phase at half-filling, we find that binding of two holes only occurs at low values of the hopping, where the holes are slow. We have theoretically verified that pair formation occurs in the limit of immobile holes, where the pure Kitaev model remains exactly solvable. When we instead fix the hopping at an intermediate, more realistic, value, and vary the Heisenberg and Kitaev interaction strengths, we find pairing tendencies only in the Néel phase. This is in contrast to prior mean-field calculations, highlighting the importance of accounting for the kinetic energy of dopants in generalized Kitaev models. Interestingly, we also find signatures of pair-density wave formation over the studied range of model parameters, namely, a periodic modulation of the charge density as well as the spin-spin and pair-pair correlations in real space. Moreover, we present a comparative study of the different correlations as a function of doping. We finally discuss the potential for experimentally observing the studied physics in quantum materials and heterostructures.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Electronic structure, magnetic properties, and pairing tendencies of the copper-based honeycomb lattice Na 2 Cu 2 TeO 6

Spin-1/2 chains with alternating antiferromagnetic (AFM) and ferromagnetic (FM) couplings have attracted considerable interest due to the topological character of their spin excitations. Here, using density functional theory and density-matrix renormalization-group (DMRG) methods, we have systematically studied the dimerized chain system Na 2 Cu 2 TeO 6 with a d 9 electronic configuration. Near the Fermi level, in the nonmagnetic phase the dominant states are mainly contributed by the Cu 3d x 2 -y 2 orbitals highly hybridized with the O 2p orbitals, leading to an “effective” single-orbital low-energy model. By calculating the relevant hoping amplitudes, we explain the size and sign of the exchange interactions in Na 2 Cu 2 TeO 6 . In addition, a single-orbital Hubbard model is constructed for this dimerized chain system where the quantum fluctuations are taken into account. Both AFM and FM couplings (leading to an ↑|-|↓-|↓-↑| state) along the chain were found in our DMRG and Lanczos calculations, in agreement with density functional theory and neutron-scattering results. The hole pairing binding energy ΔE is predicted to be negative at Hubbard U~ 11eV, suggesting incipient pairing tendencies.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2020

Thermal effects on the electronic properties of sodium electride under high pressures

Sodium is a simple metal at ambient conditions, while it transits to an electride phase at pressures above ~160 GPa along the room temperature isotherm. Here we explore the thermal effects on the electronic properties of the $hP4$ phase of sodium along the $ρ$ = 5.872 g/cm 3 isochore. We quantitatively classify this phase as an insulator based on the criterion of nearsightedness of the one-particle density matrix. Ab initio calculations suggest that the band gap of this insulator decreases with increasing temperature along the isochore, primarily because of ionic distortions; culminating in an insulator-to-metal transition upon melting at $T_m \approx 2100$ $\hbox{K}$. This transition is accompanied by residual electronic localization (in d orbitals) in the form of dynamic electron bubbles and a change in hybridization form $p–d$ to $s–p$ upon melting. This transition is explored by tracking the electronic and electro-optical properties along the isochore under consideration.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Quantum simulation of molecules without fermionic encoding of the wave function

Abstract Molecular simulations generally require fermionic encoding in which fermion statistics are encoded into the qubit representation of the wave function. Recent calculations suggest that fermionic encoding of the wave function can be bypassed, leading to more efficient quantum computations. Here we show that the two-electron reduced density matrix (2-RDM) can be expressed as a unique functional of the unencoded N -qubit-particle wave function without approximation, and hence, the energy can be expressed as a functional of the 2-RDM without fermionic encoding of the wave function. In contrast to current hardware-efficient methods, the derived functional has a unique, one-to-one (and onto) mapping between the qubit-particle wave functions and 2-RDMs, which avoids the over-parametrization that can lead to optimization difficulties such as barren plateaus. An application to computing the ground-state energy and 2-RDM of H 4 is presented.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2021

Finite and infinite matrix product states for Gutzwiller projected mean-field wave functions

Matrix product states (MPS) and “dressed” ground states of quadratic mean fields (e.g., Gutzwiller projected Slater determinants) are both important classes of variational wave functions. This latter class has played important roles in understanding superconductivity and quantum spin liquids. We present a method to obtain both the finite and infinite MPS (iMPS) representation of the ground state of an arbitrary fermionic quadratic mean-field Hamiltonian (which in the simplest case is a Slater determinant and in the most general case is a Pfaffian). We also show how to represent products of such states (e.g., determinants times Pfaffians). From this representation one can project to single occupancy and evaluate the entanglement spectra after Gutzwiller projection. We then obtain the MPS and iMPS representation of Gutzwiller projected mean-field states that arise from the variational slave-fermion approach to the S = 1 bilinear-biquadratic quantum spin chain. To accomplish this, we develop an approach to orthogonalize degenerate iMPS to find all the states in the degenerate ground-state manifold. We find the energies of the MPS and iMPS states match the variational energies closely, indicating the method is accurate and there is minimal loss due to truncation error. We then present an exploration of the entanglement spectra of projected slave-fermion states, exploring their qualitative features and finding good qualitative agreement with the respective exact ground-state spectra found from density matrix renormalization group.

1-dimensional spin chains↗

DOE OSTI2024

Revisiting Artifacts of Kohn–Sham Density Functionals for Biosimulation

We revisit the problem of unphysical charge density delocalization/fractionalization induced by the self-interaction error of common approximate Kohn–Sham (KS) density functional theory functionals on simulation of small to medium-sized proteins in a vacuum. Aside from producing unphysical electron densities and total energies, the vanishing of the HOMO–LUMO gap associated with the unphysical charge delocalization leads to an unphysical low-energy spectrum and catastrophic failure of most popular solvers for the KS self-consistent field (SCF) problem. We apply a robust quasi-Newton SCF solver to obtain solutions for some of these difficult cases. The anatomy of the charge delocalization is revealed by the natural deformation orbitals obtained from the density matrix difference between the Hartree–Fock and KS solutions; the charge delocalization not only can occur between charged fragments (such as in zwitterionic polypeptides) but also involves neutral fragments. The vanishing-gap phenomenon and troublesome SCF convergence are both attributed to the unphysical KS Fock operator eigenspectra of molecular fragments (e.g., amino acids or their side chains). Analysis of amino acid pairs suggests that the unphysical charge delocalization can be partially ameliorated by the use of some range-separated hybrid functionals but not by semilocal or standard hybrid functionals. Last, we demonstrate that solutions without the unphysical charge delocalization can be located even for semilocal KS functionals highly prone to such defects, but such solutions have non-Aufbau character and are unstable with respect to mixing of the non-overlapping “frontier” orbitals. Caution should be exercised when unexpectedly small (or vanishing) HOMO–LUMO gaps and atypical SCF convergence patterns (e.g., oscillatory) are observed in KS DFT simulations in any context (bio or otherwise).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Identifying Band Inversions in Topological Materials Using Diffusion Monte Carlo

Topological insulators are characterized by insulating bulk states and robust metallic surface states. Band inversion is a hallmark of topological insulators. At time-reversal invariant points in the Brillouin zone, spin–orbit coupling (SOC) induces a swapping of orbital character at the bulk band edges. Reliably detecting band inversion in solid-state systems with many-body methods would aid in identifying possible candidates for spintronics and quantum computing applications and improve our understanding of the physics behind topologically nontrivial systems. Density functional theory (DFT) methods are a well-established means of investigating these interesting materials due to their favorable balance of computational cost and accuracy but often struggle to accurately model the electron–electron correlations present in the many materials containing heavier elements. In this work, we develop a novel method to detect band inversion within continuum quantum Monte Carlo (QMC) methods that can accurately treat the electron correlation and spin–orbit coupling that are crucial to the physics of topological insulators. Our approach applies a momentum-space-resolved atomic population analysis throughout the first Brillouin zone utilizing the Löwdin method and the one-body reduced density matrix produced with diffusion Monte Carlo (DMC). We integrate this method into QMCPACK, an open source ab initio QMC package, so that these ground-state methods can be used to complement experimental studies and validate prior DFT work on predicting the band structures of correlated topological insulators. Here, we demonstrate this new technique on the topological insulator bismuth telluride, which displays band inversion between its Bi-p and Te-p states at the Γ-point. We show an increase in charge on the bismuth-p orbital and a decrease in charge on the tellurium-p orbital when comparing band structures with and without SOC. Additionally, we use our method to compare the degree of band inversion present in monolayer Bi 2 Te 3 , which has no interlayer van der Waals interactions, to that seen in the bilayer and bulk. The method presented here will enable future many-body studies of band inversion that can shed light on the delicate interplay between correlation and topology in correlated topological materials.

Band structure↗

DOE OSTI2024

An Exact Expression for Multidimensional Spectroscopy of a Spin‐Boson Hamiltonian

Multidimensional coherent spectroscopy is a powerful tool to characterize nonlinear optical response functions. Typically, multidimensional spectra are interpreted via a perturbative framework that straightforwardly provides intuition into the density matrix dynamics that give rise to specific spectral features. When the goal is to characterize system coupling to a thermal bath however, the perturbative formalism becomes unwieldy and yields less intuition. Here, an approach developed by Vagov et al. is extended to provide an exact expression for multidimensional spectra of a spin-boson Hamiltonian up to arbitrary order of electric field interaction. Furthermore, the utility of this expression is demonstrated by modeling polaron formation and coherent exciton-phonon coupling in quantum dots, which strongly agree with experiment.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

Quarkonium semiclassical transport in quark-gluon plasma: factorization and quantum correction

We study quarkonium transport in the quark-gluon plasma by using the potential nonrelativistic QCD (pNRQCD) effective field theory and the framework of open quantum systems. We argue that the coupling between quarkonium and the thermal bath is weak using separation of scales, so the initial density matrix of the total system factorizes and the time evolution of the subsystem is Markovian. We derive the semiclassical Boltzmann equation for quarkonium by applying a Wigner transform to the Lindblad equation and carrying out a semiclassical expansion. We resum relevant interactions to all orders in the coupling constant at leading power of the nonrelativistic and multipole expansions. The derivation is valid for both weakly coupled and strongly coupled quark-gluon plasmas. We find reaction rates in the transport equation factorize into a quarkonium dipole transition function and a chromoelectric gluon distribution function. For the differential reaction rate, the definition of the momentum dependent chromoelectric gluon distribution function involves staple-shaped Wilson lines. For the inclusive reaction rate, the Wilson lines collapse into a straight line along the real time axis and the distribution becomes momentum independent. The relation between the two Wilson lines is analogous to the relation between the Wilson lines appearing in the gluon parton distribution function (PDF) and the gluon transverse momentum dependent parton distribution function (TMDPDF). The centrality dependence of the quarkonium nuclear modification factor measured by experiments probes the momentum independent distribution while the transverse momentum dependence and measurements of the azimuthal angular anisotropy may be able to probe the momentum dependent one. We discuss one way to indirectly constrain the quarkonium in-medium real potential by using the factorization formula and lattice calculations. The leading quantum correction to the semiclassical transport equation of quarkonium is also worked out. The study can be easily generalized to quarkonium transport in cold nuclear matter, which is relevant for quarkonium production in eA collisions in the future Electron-Ion Collider.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2021

Islands in de Sitter space

We consider black holes in 2d de Sitter JT gravity coupled to a CFT, and entangled with matter in a disjoint non-gravitating universe. Tracing out the entangling matter leaves the CFT in a density matrix whose stress tensor backreacts on the de Sitter geometry, lengthening the wormhole behind the black hole horizon. Naively, the entropy of the entangling matter increases without bound as the strength of the entanglement increases, but the monogamy property predicts that this growth must level off. We compute the entropy via the replica trick, including wormholes between the replica copies of the de Sitter geometry, and find a competition between conventional field theory entanglement entropy and the surface area of extremal “islands” in the de Sitter geometry. The black hole and cosmological horizons both play a role in generating such islands in the backreacted geometry, and have the effect of stabilizing the entropy growth as required by monogamy. We first show this in a scenario in which the de Sitter spatial section has been decompactified to an interval. Then we consider the compact geometry, and argue for a novel interpretation of the island formula in the context of closed universes that recovers the Page curve. Finally, we comment on the application of our construction to the cosmological horizon in empty de Sitter space.

2D gravity↗

DOE OSTI2023

The reflected entanglement spectrum for free fermions

We consider the reflected entropy and the associated entanglement spectrum for free fermions reduced to two intervals in 1 + 1 dimensions. Working directly in the continuum theory the reflected entropy can be extracted from the spectrum of a singular integral equation whose kernel is determined by the known free fermion modular evolved correlation function. We find the spectrum numerically and analytically in certain limits. For intervals that almost touch the reflected entanglement spectrum approaches the spectrum of the thermal density matrix. This suggests that the reflected entanglement spectrum is well suited to the task of extracting physical data of the theory directly from the ground state wave function.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗