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Results for “Lattice models”

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.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Thermalization in the one-dimensional Salerno model lattice

The Salerno model constitutes an intriguing interpolation between the integrable Ablowitz-Ladik (AL) model and the more standard (nonintegrable) discrete nonlinear Schrödinger (DNLS) one. The competition of local on-site nonlinearity and nonlinear dispersion governs the thermalization of this model. Here, we investigate the statistical mechanics of the Salerno one-dimensional lattice model in the nonintegrable case and illustrate the thermalization in the Gibbs regime. As the parameter interpolating between the two limits (from DNLS toward AL) is varied, the region in the space of initial energy and norm densities leading to thermalization expands. The thermalization in the non-Gibbs regime heavily depends on the finite system size; we explore this feature via direct numerical computations for different parametric regimes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Modeling Intercalation Chemistry with Multiredox Reactions by Sparse Lattice Models in Disordered Rocksalt Cathodes

Modern battery materials can contain many elements with substantial site disorder, and their configurational state has been shown to be critical for their performance. The intercalation voltage profile is a critical parameter to evaluate the performance of energy storage. The application of commonly used cluster expansion techniques to model the intercalation thermodynamics of such systems ab initio is challenged by the combinatorial increase in configurational degrees of freedom as the number of species grows. Such challenges necessitate the efficient generation of lattice models without overfitting and proper sampling of the configurational space under the requirement of charge balance in ionic systems. In this work, we introduce a combined approach that addresses these challenges by (1) constructing a robust cluster expansion Hamiltonian using the sparse regression technique, including -norm regularization and structural hierarchy; and (2) implementing semigrand-canonical Monte Carlo to sample charge-balanced ionic configurations using the table-exchange method and an ensemble average approach. These techniques are applied to a disordered rocksalt oxyfluoride (LMNOF) that is part of a family of promising earth-abundant cathode materials. The simulated voltage profile is found to be in good agreement with experimental data and particularly provides a clear demonstration of the and oxygen contributions to the redox potential as a function of content.

25 ENERGY STORAGE↗
DOE OSTI2024

Superconductivity in a topological lattice model with strong repulsion

The highly tunable nature of synthetic quantum materials-both in the solid-state and cold atom contexts-invites examining which microscopic ingredients aid in the realization of correlated phases of matter such as superconductors. Recent experimental advances in moiré materials suggest that unifying the features of the Fermi-Hubbard model and quantum Hall systems creates a fertile ground for the emergence of such phases. Here, we introduce the "double Hofstadter"model, a minimal 2D lattice model that incorporates exactly these features: Time-reversal symmetry, band topology, and strong repulsive interactions. By using infinite cylinder density matrix renormalization group methods (cylinder iDMRG), we investigate the ground state phase diagram of this model. We find that it hosts an interaction-induced quantum spin Hall insulator and demonstrate that weakly hole-doping this state gives rise to a superconductor at a finite circumference, with indications that this behavior persists on larger cylinders. Further, at the aforementioned circumference, the superconducting phase is surprisingly robust to perturbations including additional repulsive interactions in the pairing channel. By developing a technique to probe the superconducting gap function in iDMRG, we phenomenologically characterize the superconductor. Namely, we demonstrate that it is formed from the weak pairing of holes atop the quantum spin Hall insulator. Furthermore, we determine the pairing symmetry of the superconductor, finding it to be p-wave-reminiscent of the unconventional superconductivity reported in experiments on twisted bilayer graphene (TBG). Motivated by this, we elucidate structural similarities and differences between our model and those of TBG in its chiral limit. Finally, to provide a more direct experimental realization, we detail an implementation of our Hamiltonian in a system of cold fermionic alkaline-earth atoms in an optical lattice.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Spin-lattice model for cubic crystals

In this work, we present a methodology based on the Néel model to build a classical spin-lattice Hamiltonian for cubic crystals capable of describing magnetic properties induced by the spin-orbit coupling like magnetocrystalline anisotropy and anisotropic magnetostriction, as well as exchange magnetostriction. Taking advantage of the analytical solutions of the Néel model, we derive theoretical expressions for the parametrization of the exchange integrals and Néel dipole and quadrupole terms that link them to the magnetic properties of the material. This approach allows us to build accurate spin-lattice models with the desired magnetoelastic properties. We also explore a possible way to model the volume dependence of magnetic moment based on the Landau energy. This feature allows us to consider the effects of hydrostatic pressure on the saturation magnetization. We apply this method to develop a spin-lattice model for BCC Fe and FCC Ni, and we show that it accurately reproduces the experimental elastic tensor, magnetocrystalline anisotropy under pressure, anisotropic magnetostrictive coefficients, volume magnetostriction, and saturation magnetization under pressure at zero temperature. This work could constitute a step towards large-scale modeling of magnetoelastic phenomena.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Lattice modeling of excavation damage in argillaceous clay formations: Influence of deformation and strength anisotropy

This paper presents modeling of mechanical anisotropy in argillaceous rocks using an irregular lattice modeling approach, namely the rigid-body-spring network. To represent the mechanical anisotropy, new schemes are implemented in the modeling framework. The directionality of elastic deformation is resolved by modifying the element formulation with anisotropic elastic properties. The anisotropy of strength and failure characteristics is facilitated by adopting orientation-dependent failure criteria into the failure model. The verification of the improved modeling procedures is performed against theoretical model predictions for unconfined compression tests with various bedding orientations. Furthermore, excavation damage and fracturing processes in rock formations are simulated for different geomechanical configurations, such as rock anisotropy and tectonic heterogeneity. The simulated excavation damage characteristics are realistic and comparable with the actual field observation at a tunnel located in an argillaceous clay formation. The simulation results provide insights into the excavation damage zone phenomena with an explicit representation of fracturing processes.

58 GEOSCIENCES↗
DOE OSTI2023

Skyrmion crystals in the triangular Kondo lattice model

We present a systematic study of the formation of skyrmion crystals in a triangular Kondo Lattice model for generic electron filling fractions. Our results indicate that the four-sublattice chiral antiferromagnetic ordering that was reported more than one decade ago can be understood as the dense limit of a sequence of skyrmion crystals whose lattice parameter is dictated by the Fermi wave-vector. This observation has important implications for the ongoing search of skyrmion crystals in metallic materials with localized magnetic moments.

Wang, Zhentao↗
DOE OSTI2020

Coupled dimer and bond-order-wave order in the quarter-filled one-dimensional Kondo lattice model

Motivated by experiments on the organic compound (Per) 2 [Pt(mnt) 2 ], we study the ground state of the onedimensional Kondo lattice model at quarter filling with the density matrix renormalization group method. Here, we show a coupled dimer and bond-order-wave (BOW) state in the weak-coupling regime for the localized spins and itinerant electrons, respectively. The quantum phase transitions for the dimer and the BOW orders occur at the same critical coupling parameter J c , with the opening of a charge gap. The emergence of the combination of dimer and BOW order agrees with the experimental findings of the simultaneous Peierls and spin-Peierls transitions at low temperatures, which provides a theoretical understanding of such a phase transition. We also show that the localized spins in this insulating state have quasi-long-ranged spin correlations with collinear configurations, which resemble the classical dimer order in the absence of a magnetic order.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Lattice model of heavy-light three-body system

We present a study of a $1+1$ dimensional heavy-light three-body system in finite volume. The heavy-light system is simulated by a coupled-channel $\phi^4$ type lattice model, and both ground state and excited states of multiparticle energy spectra are measured on various lattices. The lattice simulation data analysis is performed based on variational approach.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

A microscopic Kondo lattice model for the heavy fermion antiferromagnet CeIn 3

Electrons at the border of localization generate exotic states of matter across all classes of strongly correlated electron materials and many other quantum materials with emergent functionality. Heavy electron metals are a model example, in which magnetic interactions arise from the opposing limits of localized and itinerant electrons. This remarkable duality is intimately related to the emergence of a plethora of novel quantum matter states such as unconventional superconductivity, electronic-nematic states, hidden order and most recently topological states of matter such as topological Kondo insulators and Kondo semimetals and putative chiral superconductors. The outstanding challenge is that the archetypal Kondo lattice model that captures the underlying electronic dichotomy is notoriously difficult to solve for real materials. Here we show, using the prototypical strongly-correlated antiferromagnet CeIn 3 , that a multi-orbital periodic Anderson model embedded with input from ab initio bandstructure calculations can be reduced to a simple Kondo-Heisenberg model, which captures the magnetic interactions quantitatively. We validate this tractable Hamiltonian via high-resolution neutron spectroscopy that reproduces accurately the magnetic soft modes in CeIn 3 , which are believed to mediate unconventional superconductivity. Our study paves the way for a quantitative understanding of metallic quantum states such as unconventional superconductivity.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Kondo Lattice Model of Magic-Angle Twisted-Bilayer Graphene: Hund’s Rule, Local-Moment Fluctuations, and Low-Energy Effective Theory

For this work, we apply a generalized Schrieffer-Wolff transformation to the extended Anderson-like topological heavy fermion (THF) model for the magic-angle (θ=1.05°) twisted bilayer graphene (MATBLG) [Phys. Rev. Lett. 129, 047601 (2022)], to obtain its Kondo lattice limit. In this limit localized $\mathcal{f}$ electrons on a triangular lattice interact with topological conduction $\mathcal{c}$ electrons. By solving the exact limit of the THF model, we show that the integer fillings ν=0, ±1, ±2 are controlled by the heavy $\mathcal{f}$ electrons, while ν=±3 is at the border of a phase transition between two $\mathcal{f}$-electron fillings. For ν=0, ±1, ±2, we then calculate the Ruderman-Kittel-Kasuya-Yosida (RKKY) interactions between the $\mathcal{f}$ moments in the full model and analytically prove the SU(4) Hund’s rule for the ground state which maintains that two $\mathcal{f}$ electrons fill the same valley-spin flavor. Our (ferromagnetic interactions in the) spin model dramatically differ from the usual Heisenberg antiferromagnetic interactions expected at strong coupling. We show the ground state in some limits can be found exactly by employing a positive semidefinite “bond-operators” method. We then compute the excitation spectrum of the $\mathcal{f}$ moments in the ordered ground state, prove the stability of the ground state favored by RKKY interactions, and discuss the properties of the Goldstone modes, the (reason for the accidental) degeneracy of (some of) the excitation modes, and the physics of their phase stiffness. We develop a low-energy effective theory for the $\mathcal{f}$ moments and obtain analytic expressions for the dispersion of the collective modes. We discuss the relevance of our results to the spin-entropy experiments in TBG.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Modeling lattice rotation fields from discrete crystallographic slip bands in superalloys

Here in this work, we investigate the relationship between an intense slip band (ISB) and the zone of large lattice rotations that forms ahead of the tip of the ISB. We develop a crystal plasticity finite element model of a discrete ISB lying within an oligocrystalline assembly and calculate the local crystalline stress and lattice rotation fields generated by the ISB. The calculations demonstrate that, first, a region of severe lattice rotations, commonly referred to as a microvolume, does not form without the ISB, and second, large amounts of accumulated slip in the ISB are required to enlarge the microvolume to sizes and rotation magnitudes observed experimentally. Ahead of the ISB tip, the quintessential plastic zone always forms, but the atypical microvolume forms when non-concentrated and spatially diffuse slip is activated by the ISB-induced stress field. This result suggests that the detrimental ISB/microvolume pair will likely appear in pairs of crystals in which transmission of the slip from the ISB is severely blocked by the grain boundary, a hypothesis that we verify with a few target cases.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Magnon orbital angular momentum of ferromagnetic honeycomb and zigzag lattice models

By expanding the gauge 𝜆 𝑛 ⁡(𝐤) for magnon band 𝑛 in harmonics of momentum 𝐤=(𝑘,𝜙), we demonstrate that the only observable component of the magnon orbital angular momentum 𝑂 𝑛 ⁡(𝐤) is its angular average over all angles 𝜙, denoted by 𝐹 𝑛 ⁡(𝑘). Although 𝐹 𝑛 ⁡(𝑘) vanishes for antiferromagnetic honeycomb and zigzag (0<𝐽 1 <𝐽 2 ) lattices, it is nonzero for the ferromagnetic (FM) versions of those lattices in the presence of Dzyaloshinskii-Moriya interactions. For a FM zigzag model with equal exchange interactions 𝐽 1⁢𝑥 and 𝐽 1⁢𝑦 along the 𝑥 and 𝑦 axes, the magnon bands are degenerate along the boundaries of the Brillouin zone with 𝑘 𝑥 −𝑘 𝑦 =±𝜋/𝑎 and the Chern numbers 𝐶 𝑛 are not well defined. However, a revised model with 𝐽 1⁢𝑦 ≠𝐽 1⁢𝑥 lifts those degeneracies and produces well-defined Chern numbers of 𝐶𝑛=±1 for the two magnon bands. When 𝐽 1⁢𝑦 =𝐽 1⁢𝑥 , the thermal conductivity 𝜅 𝑥⁢𝑦⁡ (𝑇) of the FM zigzag lattice is largest for 𝐽2/𝐽1>6 but is still about four times smaller than that of the FM honeycomb lattice at high temperatures. Due to the removal of band degeneracies, 𝜅𝑥⁢𝑦⁡(𝑇) is slightly enhanced when 𝐽 1⁢𝑦 ≠𝐽 1⁢𝑥 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Emergent quantum mechanics at the boundary of a local classical lattice model

We formulate a model in which quantum mechanics emerges from classical mechanics. Given a local Hamiltonian H acting on n qubits, we define a local classical model with an additional spatial dimension whose boundary dynamics is approximately—but to arbitrary precision—described by Schrödinger's equation and H. The bulk consists of a lattice of classical bits that propagate towards the boundary through a circuit of stochastic matrices. The bits reaching the boundary are governed by a probability distribution whose deviation from the uniform distribution can be interpreted as the quantum-mechanical wave function. Bell nonlocality is achieved because information can move through the bulk much faster than the boundary speed of light. Finally, we analytically estimate how much the model deviates from quantum mechanics, and we validate these estimates using computer simulations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Dedicated beam position monitor pair for model-independent lattice characterization at NSLS-II

This paper reports recent lattice characterization results obtained at the National Synchrotron Light Source II (NSLS-II) storage ring, conducted without reliance on a lattice model. A pair of beam position monitors (BPMs) with bunch-by-bunch (B×B) resolution, were recently installed in a section of the storage ring free of magnetic fields. The new BPM pair measured the beam, or bunch’s transverse Poincar´e map precisely after the beam was excited. Linear one-turn-matrices (OTM) were then derived, and from these, the 4-dimensional coupled Twiss parameters were extracted at the locations of the BPM pair. By normalizing beam oscillation amplitudes with the Twiss parameters, the global action-variables were obtained. These action-variables facilitated the measurement of the local Twiss parameters observed by other BPMs independent on lattice model. This method is general, and particularly useful in certain scenarios such as a round beam mode in a diffraction-limited light source ring. We applied it to assess both weakly and strongly coupled lattices at the NSLS-II ring. Through analysis of the strongly coupled lattice, the quadrupole tilt errors were estimated to be less than 400 µrad. Utilizing the BPMs’ B×B resolution, for the first time we observed the variations of the linear lattice along a long bunch-train.

43 PARTICLE ACCELERATORS↗
DOE OSTI2024

Dedicated beam position monitor pair for model-independent lattice characterization at NSLS-II

This paper reports recent lattice characterization results obtained at the National Synchrotron Light Source II (NSLS-II) storage ring, conducted without reliance on a lattice model. A pair of beam position monitors (BPMs) with bunch-by-bunch (B$\times$B) resolution, were recently installed in a section of the storage ring free of magnetic fields. The new BPM pair measured the beam, or bunch’s transverse Poincaré map precisely after the beam was excited. Linear one-turn-matrices (OTM) were then derived, and from these, the 4-dimensional coupled Twiss parameters were extracted at the locations of the BPM pair. By normalizing beam oscillation amplitudes with the Twiss parameters, the global action-variables were obtained. Additionally, these action-variables facilitated the measurement of the local Twiss parameters observed by other BPMs independent on lattice model. This method is general, and particularly useful in certain scenarios such as a round beam mode in a diffraction-limited light source ring. We applied it to assess both weakly and strongly coupled lattices at the NSLS-II ring. Through analysis of the strongly coupled lattice, the quadrupole tilt errors were estimated to be less than 400 μrad. Utilizing the BPMs’ B$\times$B resolution, for the first time we observed the variations of the linear lattice along a long bunch-train.

36 MATERIALS SCIENCE↗