arXiv subjects

J. Tinka Gammel

Publications and source records attributed to J. Tinka Gammel.

14 recordsLinked to original sources

arXiv2024

Neural Network Representations of Multiphase Equations of State

Equations of State model relations between thermodynamic variables and are ubiquitous in scientific modelling, appearing in modern day applications ranging from Astrophysics to Climate Science. The three desired properties of a general Equation of State model are adherence to the Laws of Thermodynamics, incorporation of phase transitions, and multiscale accuracy. Analytic models that adhere to all three are hard to develop and cumbersome to work with, often resulting in sacrificing one of these elements for the sake of efficiency. In this work, two deep-learning methods are proposed that provably satisfy the first and second conditions on a large-enough region of thermodynamic variable space. The first is based on learning the generating function (thermodynamic potential) while the second is based on structure-preserving, symplectic neural networks, respectively allowing modifications near or on phase transition regions. They can be used either "from scratch" to learn a full Equation of State, or in conjunction with a pre-existing consistent model, functioning as a modification that better adheres to experimental data. We formulate the theory and provide several computational examples to justify both approaches, and highlight their advantages and shortcomings.

physics.comp-ph↗

arXiv1998

Signatures of Stripe Phases in Hole Doped $La_2NiO_4$

We study nickelate-centered and oxygen-centered stripe phases in doped La$_{2}$NiO$_{4}$ materials. We use an inhomogeneous Hartree-Fock and random-phase approximation approach including both electron-electron and electron-lattice(e-l) coupling for a layer of La$_{2}$NiO$_{4}$. We find that whether the ground state after commensurate hole doping comprises Ni-centered or O-centered charge-localized stripes depends sensitively on the e-l interaction. With increasing e-l interaction strength, a continuous transition from an O-centered stripe phase to a Ni-centered one is found. Various low- and high-energy signatures of these two kinds of stripe phases are predicted, which can clearly distinguish them. These signatures reflect the strongly correlated spin-charge-lattice features in the vicinity of Ni-centered or O-centered stripe domains. The importance of e-l interaction for recent experiments on stripe phases is discussed.

cond-mat.supr-con↗

arXiv1997

Modeling Metallic Microstructure Using Moving Finite Elements

We present an efficient method for anealing 3d metallic grains using Gradient Weighted Moving Finite Elements (GWMFE). The initial grain microstructure is generated from Monte-Carlo evolution of a an effective discrete model on the initial (frozen) unstructured grid generated for the external geometry of the GWMFE calculation.

physics.comp-ph↗

arXiv1996

Quantum Breathers in a Nonlinear Lattice

We study nonlinear phonon excitations in a one-dimensional quantum nonlinear lattice model using numerical exact diagonalization. We find that multi-phonon bound states exist as eigenstates which are natural counterparts of breather solutions of classical nonlinear systems. In a translationally invariant system, these quantum breather states form particle-like bands and are characterized by a finite correlation length. The dynamic structure factor has significant intensity for the breather states, with a corresponding quenching of the neighboring bands of multi-phonon extended states.

cond-mat↗

arXiv1994

Pressure Tuning of the Charge Density Wave in the Halogen-Bridged Transition-Metal (MX) Solid $Pt_2Br_6(NH_3)_4$

We report the pressure dependence up to 95 kbar of Raman active stretching modes in the quasi-one-dimensional MX chain solid $Pt_2Br_6(NH_3)_4$. The data indicate that a predicted pressure-induced insulator-to-metal transition does not occur, but are consistent with the solid undergoing either a three-dimensional structural distortion, or a transition from a charge-density wave to another broken-symmetry ground state. We show that such a transition cacan be well-modeled within a Peierls-Hubbard Hamiltonian. 1993 PACS: 71.30.+h, 71.45.Lr, 75.30.Fv, 78.30.-j, 81.40.Vw

cond-mat↗

arXiv1994

Improved Mean-Field Scheme for the Hubbard Model

Ground state energies and on-site density-density correlations are calculated for the 1-D Hubbard model using a linear combination of the Hubbard projection operators. The mean-field coefficients in the resulting linearized Equations of Motion (EOM) depend on both one-particle static expectation values as well as static two-particle correlations. To test the model, the one particle expectation values are determined self-consistently while using Lanczos determined values for the two particle correlation terms. Ground state energies and on-site density-density correlations are then compared as a function of $U$ to the corresponding Lanczos values on a 12 site Hubbard chain for 1/2 and 5/12 fillings. To further demonstrate the validity of the technique, the static correlation functions are also calculated using a similar EOM approach, which ignores the effective vertex corrections for this problem, and compares those results as well for a 1/2 filled chain. These results show marked improvement over standard mean-field techniques.

cond-mat↗

arXiv1994

Comment on Tuning of the CDW in MX Chains

In M. Alouani et al., Phys. Rev. Lett. 71, 1415 (1993), the authors performed local-density-approximation (LDA) calculations and fit to the two-band model [J.T. Gammel et al., Phys. Rev. B 45, 6408 (1992)] we proposed for halogen-bridged transition-metal linear-chain compounds ($M$$X$ chains). Based on that fit, the authors argue a hard-core repulsive term must be added to the lattice potential in our model. However, the authors fit only to the variation in total energy as a function of percent dimerization for a fixed $M$$M$ distance and did not fit the variation in total energy with $M$$M$ distance. Thus the fit was incorrectly calculated, the LDA total energy surface is {\it not} reproduced by the parameters listed in this paper, and the conclusion as to the importance of anharmonic corrections must be reexamined. In contradiction to their conclusion based on this erroneous fit, I show here that the harmonic approximation (linear $M$$X$ springs to model the lattice energy) is in fact very good, and a small quartic correction yields quantitative agreement with the LDA total energy, though to this order more realistic electron-phonon interactions should be included in the model, as discussed in I. Batistic et al., Phys. Rev. B 48, 6065 (1993). 1992 PACS: 71.38.+i, 71.25.Tn, 71.20.Hk

cond-mat↗

arXiv1993

Infinite Volume Extrapolations of Finite Cluster Calculations, ---How Correct are These?

Extrapolations of numerical data obtained from finite cluster calculations to the infinite volume limit can often give incorrect results. We discuss four separate cases: (a) the intensity of the lowest two-photon absorption in the infinite polyene, (b) bond alternation in the infinite polyene, (c) Cooper type pairing in the simple Hubbard model, and (d) pairing within the extended Hubbard model.

cond-mat↗

arXiv1992

Spin-Peierls ground states and frustration in a multi-band Peierls-Hubbard model

We discuss the consequences of including both electron-phonon and electron-electron couplings in multi-band models, focusing on numerical studies of a one-dimensional two-band model in the intermediate regime for both coupling strengths. Spin-Peierls as well as long-period, frustrated ground states are identified, reminisent of those found in antiferromagnetic next-nearest neighbor (ANNNI) models. We speculate on experimentally observable signatures of this rich phase diagram. 1992 PACS: 75.30.Fv, 71.45.Lr, 71.38+i, 64.70.Rh

cond-mat↗

arXiv1992

A Non-Standard Quark Model and the Mass Difference $Ξ^- - Ξ^0$

We show that a highly unconventional theory, based on the 16 dimensional (${3\over2}$,${3\over2}$) irreducible representation of O(4), fits the masses of the baryons $Ξ^-$,$Ξ^0$,$Σ^-$,$Σ^0$,$Σ^+$,$Λ$,$p$,$n$ and the leptons $μ$,$e$,$ν_μ$,$ν_e$ to within current experimental error, yet yields a prediction substantially different from that of Coleman and Glashow, namely $Ξ^- - Ξ^0 < 6.1$ MeV. We discuss the ramifications of this very non-standard model in the hope to stimulate improved measurements of the $Ξ^- - Ξ^0$ mass difference.

hep-ph↗

arXiv1992

Extracting Infinite System Properties from Finite Size Clusters: `Phase Randomization/Boundary Condition Averaging'

When electron-electron correlations are important, it is often necessary to use exact numerical methods, such as Lanczos diagonalization, to study the full many-body Hamiltonian. Unfortunately, such exact diagonalization methods are restricted to small system sizes. We show that if the Hubbard $U$ term is replaced by a ``periodic Hubbard" term, the full many body Hamiltonian may be numerically exactly solved, even for very large systems (even $>$100 sites), though only for low fillings. However, for half-filled systems and large $U$ this approach is not only no longer exact, it no longer improves extrapolation to larger systems. We discuss how generalized ``randomized variable averaging'' (RVA) or ``phase randomization'' schemes can be reliably employed to improve extrapolation to large system sizes in this regime. This general approach can be combined with any many-body method and is thus of broad interest and applicability.

cond-mat↗

arXiv1992

Electron-Phonon Driven Spin Frustration in Multi-Band Hubbard Models: MX Chains and Oxide Superconductors

We discuss the consequences of both electron-phonon and electron-electron couplings in 1D and 2D multi-band (Peierls-Hubbard) models. After briefly discussing various analytic limits, we focus on (Hartree-Fock and exact) numerical studies in the intermediate regime for both couplings, where unusual spin-Peierls as well as long-period, frustrated ground states are found. Doping into such phases or near the phase boundaries can lead to further interesting phenomena such as separation of spin and charge, a dopant-induced phase transition of the global (parent) phase, or real-space (``bipolaronic'') pairing. We discuss possible experimentally observable consequences of this rich phase diagram for halogen-bridged, transition metal, linear chain complexes (MX chains) in 1D and the oxide superconductors in 2D.

cond-mat↗

arXiv1992

Photoinduced charge separation in Q1D heterojunction materials: Evidence for electron-hole pair separation in mixed-halide $MX$ solids

Resonance Raman experiments on doped and photoexcited single crystals of mixed-halide $MX$ complexes ($M$=Pt; $X$=Cl,Br) clearly indicate charge separation: electron polarons preferentially locate on PtBr segments while hole polarons are trapped within PtCl segments. This polaron selectivity, potentially very useful for device applications, is demonstrated theoretically using a discrete, 3/4-filled, two-band, tight-binding, extended Peierls-Hubbard model. Strong hybridization of the PtCl and PtBr electronic bands is the driving force for separation.

cond-mat↗

arXiv1992

Relaxed Excited State Geometries in a Peierls-Hubbard Model for Polyenes

Using parameter values relevant to polyacetylene and its finite polyene analogs, we determine, via exact finite size diagonalization of a 1D Peierls-Hubbard model, the relaxed geometry and optical absorption spectra of several states of interest in optical experiments (the singlet ($1^1A_g$) and triplet ($1^3B_u$) ground states, the singlet one ($n^1B_u$) and two ($2^1A_g$) photon gaps, and the triplet one ($n^3A_g$) photon gap) in order to examine the question of how well this simple model can really capture the behavior of this simple material.

cond-mat↗