Ground Model Research Articles

Ground-state and spectral properties of the doped one-dimensional optical Hubbard-Su-Schrieffer-Heeger model

We present a density matrix renormalization group study of the doped one-dimensional (1D) Hubbard-Su-Schrieffer-Heeger (Hubbard-SSH) model, where the atomic displacements linearly modulate the nearest-neighbor hopping integrals. Focusing on an optical variant of the model in the strongly correlated limit relevant for cuprate spin chains, we examine how the SSH interaction modifies the model's ground- and excited-state properties. The SSH coupling weakly renormalizes the model's single- and two-particle response functions for electron-phonon $(e\text{\ensuremath{-}}\mathrm{ph})$ coupling strengths below a parameter-dependent critical value ${g}_{\mathrm{c}}$. For larger $e\text{\ensuremath{-}}\mathrm{ph}$ coupling, the sign of the effective hopping integrals changes for a subset of orbitals, which drives a lattice dimerization distinct from the standard nesting-driven picture in 1D. The spectral weight of the one- and two-particle dynamical response functions are dramatically rearranged across this transition, with significant changes in the ground-state correlations. We argue that this dimerization results from the breakdown of the linear approximation for the $e\text{\ensuremath{-}}\mathrm{ph}$ coupling and thus signals a fundamental limitation of the linear SSH interaction. Our results have consequences for our understanding of how SSH-like interactions can enter the physics of strongly correlated quantum materials, including the recently synthesized doped cuprate spin chains.

Constructing Hubbard models for the hydrogen chain using sliced-basis density matrix renormalization group

Sliced-basis DMRG(sb-DMRG) is used to simulate a chain of hydrogen atoms and to construct low-energy effective Hubbard-like models. The downfolding procedure first involves a change of basis to a set of atom-centered Wannier functions constructed from the natural orbitals of the exact DMRG one-particle density matrix. The Wannier function model is then reduced to a fewer-parameter Hubbard-like model, whose parameters are determined by minimizing the expectation value of the Wannier Hamiltonian in the ground state of the Hubbard Hamiltonian. This indirect variational procedure not only yields compact and simple models for the hydrogen chain, but also allows us to explore the importance of constraints in the effective Hamiltonian, such as the restricting the range of the single-particle hopping and two-particle interactions, and to assess the reliability of more conventional downfolding. The entanglement entropy for a model's ground state, cut in the middle, is an important property determining the ability of DMRG and tensor networks to simulate the model, and we study its variation with the range of the interactions. Counterintuitively, we find that shorter ranged interactions often have larger entanglement.

In-situ acoustic monitoring of direct energy deposition process with deep learning-assisted signal denoising

In-situ monitoring is crucial for detecting process anomalies and ensuring part quality in additive manufacturing. Acoustic-based monitoring techniques offer extra benefits such as adjustable sensor setup and lower hardware costs. In the direct energy deposition (DED) process, acoustic signals generated by laser-material interactions carry information about underlying complex physical mechanisms such as melting, solidification, crack propagation, and pore formation. This paper presents a novel acoustic-based in-situ monitoring method for the DED process. The raw acoustic signal is made up of laser-material interaction sound as well as noise from machine movement, inert gas flow, and powder flow. A deep learning model is developed to build an end-to-end signal denoising framework to minimize environmental noise and extract the laser-material interaction sound. Audio equalization, bandpass filtering, and Harmonic-Percussive Source Separation algorithm are used to produce a cleaned laser-material interaction sound as the model's ground truth target. Acoustic data is collected from experiments using different DED machines, materials, and varied process parameters to train the deep learning model. The proposed deep learning-assisted signal denoising strategy lays the groundwork for acoustic-based in-situ defect detection of the DED process.

Auxiliary field quantum Monte Carlo for multiband Hubbard models: Controlling the sign and phase problems to capture Hund's physics

In the study of strongly-correlated, many-electron systems, the Hubbard Kanamori (HK) model has emerged as one of the prototypes for transition metal oxide physics. The model is multi-band in nature and contains Hund's coupling terms, which have pronounced effects on metal-insulator transitions, high-temperature superconductivity, and other physical properties. In the following, we present a complete theoretical framework for treating the HK model using the ground state Auxiliary Field Quantum Monte Carlo (AFQMC) method and analyze its performance on few-band models whose parameters approximate those observed in ruthenate, rhodates, and other materials exhibiting Hund's physics. Unlike previous studies, the constrained path and phaseless approximations are used to respectively control the sign and phase problems, which enables high accuracy modeling of the HK model's ground state properties within parameter regimes of experimental interest. We demonstrate that, after careful consideration of the Hubbard-Stratonovich transformations and trial wave functions employed, relative errors in the energy of less than 1% can routinely be achieved for moderate to large values of the Hund's coupling constant. Crucially, our methodology also accurately predicts magnetic ordering and phase transitions. The results presented open the door to more predictive modeling of Hund's physics within a wide range of strongly-correlated materials using AFQMC.

Data-Driven Synthetic Cerebrovascular Models For Validation Of Segmentation Algorithms.

We introduce a novel method to generate biologically grounded synthetic cerebrovasculature models in a datadriven fashion. First, the centerlines of vascular filaments embedded in an acquired imaging volume are obtained by a segmentation algorithm. That imaging volume is reconstructed from a graph encoding of the centerline (i.e., generating the model's ground truth) and the segmentation algorithm is applied to the resultant volume. As the location and characteristics of the vasculature embedded in this volume are known,theaccuracyofthesegmentationalgorithmcanbeassessed. Moreover, because the synthetic volume was reconstructed directly from biological data, an assessment is made on embedded filaments that are representative of the topologicalandgeometricalcharacteristicsofthedataset. Webelieve thatsuchmodels will provide the means necessary for the enhanced evaluation of vascular segmentation algorithms.

Rigorous Results Concerning the Holstein–Hubbard Model

The Holstein model has been widely accepted as a model comprising electrons interacting with phonons; analysis of this model's ground states was accomplished two decades ago. However, the results were obtained without completely taking repulsive Coulomb interactions into account. Recent progress has made it possible to treat such interactions rigorously; in this paper, we study the Holstein--Hubbard model with repulsive Coulomb interactions. The ground state properties of the model are investigated; in particular, the ground state of the Hamiltonian is proven to be unique for an even number of electrons on a bipartite connected lattice. In addition, we provide a rigorous upper bound on charge susceptibility.

Finite element analysis (FEA) as a model to predict effects of farriery on the equine hoof.

A finite element (FE) hoof capsule was built as a small, symmetrical forelimb hoof on IDEAS* as a model for calculation and visualisation of stress and displacement of the equine hoof capsule. The model's loading was performed according to the suspension of the coffin bone within the hoof wall (pulling force) and over the sole and frog (compressing force) with a total of 3000 N. Restraints of the model's ground nodes and surface wall nodes were defined for simulation of 4 shoeing situations: a regular horseshoe, a horseshoe with a toe clip, a horseshoe with regular side clips and a horseshoe with a toe clip and more caudally-placed side clips, all fixed to the hoof capsule with 3 nails on each side and each calculated in a tense and a loose nailed condition. Von Mises stresses were taken ranging from 1.22 N/mm2 in the weightbearing border of the side clip shoe fixed loosely to the capsule up to 16.67 N/mm2 in the hoof horn material surrounding the third nail. Further high stress zones were calculated in the proximal dorsal wall, the distal heel and the lateral hoof wall. Displacement values were taken showing movements of hoof wall, sole and frog according to the shoeing conditions. Maximal displacement was calculated in the hoof capsule shod with a regular horseshoe without a clip. Minimal displacement was found in the capsule with a toe clip and 2 side clips placed behind the 3rd nail. All models showed higher displacements when calculated with a loose nail fixation. Validation of the detailed features of the models is not yet possible. Finite element analysis (FEA) can be used practically to predict influences of various farrier techniques on the equine hoof in order to avoid possible harm to horses' feet in field studies.

Multiatom interactions in the fcc Ising binary alloy: Low-temperature behavior and Monte Carlo simulations.

We investigate an Ising model of an ordering binary alloy on the face-centered-cubic lattice, such as Cu-Au. This model contains multiatom interactions on the triangles and tetrahedra of the lattice as well as the usual repulsions on the nearest-neighbor bonds. We examine the model's ground states and its low-temperature equilibrium states: There are an infinite number of the former but only a few of the latter. We also study its phase diagram using Monte Carlo simulations, which confirm the broad conclusions of previous cluster-variation-method calculations, particularly near stoichiometry. Even small triangular interactions can introduce dramatic asymmetry into the phase diagram, making it similar to those observed in real alloys.