arXiv subjects

Chris A. Marianetti

Publications and source records attributed to Chris A. Marianetti.

At least 19 recordsLinked to original sources

arXiv2025

Mott transition from the non-analyticity of the one-body reduced density-matrix functional

One-body reduced density-matrix functional (1RDMF) theory has yielded promising results for small systems such as molecules, but has not addressed quantum phase transitions such as the Mott transition. Here we explicitly execute the constrained search within a variational ansatz to construct a 1RDMF for the multi-orbital Hubbard model with up to seven orbitals in the thermodynamic limit. The variational ansatz is the \mathcal{N}=3 ansatz of the variational discrete action theory (VDAT), which can be exactly evaluated in d=\infty. The resulting 1RDMF exactly encapsulates the \mathcal{N}=3 VDAT results, which accurately captures Mott and Hund physics. We find that non-analytic behavior emerges in our 1RDMF at fixed integer filling, which gives rise to the Mott transition. We explain this behavior by separating the constrained search into multiple stages, illustrating how a nonzero Hund exchange drives the continuous Mott transition to become first-order. Our approach creates a new path forward for constructing an accurate 1RDMF for strongly correlated electron materials.

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arXiv2025

Qubit parametrization of the variational discrete action theory for the multiorbital Hubbard model

The variational discrete action theory (VDAT) at \mathcal{N}=3 is a potent tool for accurately capturing Mott and Hund physics at zero temperature in d=\infty at a cost comparable to the Gutzwiller approximation, which is recovered by VDAT at \mathcal{N}=2. Here we develop a qubit parametrization of the gauge constrained algorithm of VDAT at \mathcal{N}=3 for the multiorbital Hubbard model with general density-density interactions. The qubit parametrization yields an explicit variational trial energy, and the variational parameters consist of the momentum density distribution, the shape of a reference fermi surface, and the pure state of a qubit system with dimension of the local Hilbert space. To illustrate the power of the qubit parametrization, we solve for the ground state properties of the multiorbital Hubbard model with Hund coupling for local orbital number N_{orb}=2-7. A Taylor series expansion of the partially optimized trial energy is used to explain how the Hund's coupling changes the order of the Mott transition. For the case of the SU(2N_{orb}) Hubbard model, an explicit approach for computing the critical U_{c} for the Mott transition is provided, yielding an analytical expression for U_{c} in the large N_{orb} limit. Additionally, we provide an analytical solution for the ground state properties of the single band Hubbard model with a special density of states. Finally, we demonstrate that the qubit parametrization can also be applied to \mathcal{N}=2, for both G-type and B-type variants, where the G-type yields an identical expression to the slave spin mean-field theory. The qubit parametrization not only improves the efficiency and transparency of VDAT at \mathcal{N}=3, but also provides the key advances for the construction of a one-body reduced density matrix functional capable of capturing Mott and Hund physics.

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arXiv2025

Parameterizing empirical interatomic potentials for predicting thermophysical properties via an irreducible derivative approach: the case of ThO$_2$ and UO$_2$

The accuracy of classical physical property predictions using molecular dynamics simulations is determined by the quality of the interatomic potentials. Here we introduce a training approach for empirical interatomic potentials (EIPs) which is well suited for capturing phonons and phonon-related properties. Our approach is based on direct comparisons of the second- and third-order irreducible derivatives between an EIP and the Born-Oppenheimer potential within density functional theory (DFT) calculations. Irreducible derivatives fully exploit space group symmetry and allow for training without redundant information. We demonstrate the fidelity of our approach in the context of ThO$_2$ and UO$_2$, where we optimize parameters of an embedded-atom method potential in addition to core-shell interactions. Our EIPs provide thermophysical properties in good agreement with DFT and outperform widely utilized EIPs for phonon dispersion and thermal conductivity predictions. Reasonable estimates of thermal expansion and formation energies of Frenkel pairs are also obtained.

cond-mat.mtrl-sci↗

arXiv2024

Benchmarking phonon anharmonicity in machine learning interatomic potentials

Machine learning approaches have recently emerged as powerful tools to probe structure-property relationships in crystals and molecules. Specifically, Machine learning interatomic potentials (MLIP) can accurately reproduce first-principles data at a cost similar to that of conventional interatomic potential approaches. While MLIP have been extensively tested across various classes of materials and molecules, a clear characterization of the anharmonic terms encoded in the MLIP is lacking. Here, we benchmark popular MLIP using the anharmonic vibrational Hamiltonian of ThO$_2$ in the fluorite crystal structure. This anharmonic Hamiltonian was constructed from density functional theory (DFT) using our highly accurate and efficient irreducible derivative methods, and then used to generate molecular dynamics trajectories. This data set was used to train three classes of MLIP: Gaussian Approximation Potentials, Artificial Neural Networks (ANN), and Graph Neural Networks (GNN). The results were assessed by directly comparing phonons and their interactions, as well as phonon linewidths, phonon lineshifts, and thermal conductivity. The models were also trained on a DFT molecular dynamics dataset, demonstrating good agreement up to fifth-order for the ANN and GNN. Our analysis demonstrates that MLIP have great potential for accurately characterizing anharmonicity in materials systems at a fraction of the cost of conventional first principles-based approaches.

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arXiv2024

Ab initio elasticity at finite temperature and stress in ferroelectrics

Computing the temperature and stress dependence of the full elastic constant tensor from first-principles in non-cubic materials remains a challenging problem. Here we circumvent the aforementioned challenge via the generalized quasiharmonic approximation in conjunction with the irreducible derivative approach for computing strain dependent phonons using finite difference, explicitly including dipole-quadrupole contributions. We showcase this approach in ferroelectric PbTiO$_3$ using density functional theory, computing all independent elastic constants and piezoelectric strain coefficients at finite temperature and stress. There is good agreement between the quasiharmonic approximation and the experimental lattice parameters close to 0 K. However, the quasiharmonic approximation overestimates the temperature dependence of the lattice parameters and elastic constant tensor, demonstrating that a higher level of strain dependent anharmonic vibrational theory is needed.

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arXiv2024

Phonon thermal transport in UO$_2$ via self-consistent perturbation theory

Computing thermal transport from first-principles in UO$_2$ is complicated due to the challenges associated with Mott physics. Here we use irreducible derivative approaches to compute the cubic and quartic phonon interactions in UO$_2$ from first-principles, and we perform enhanced thermal transport computations by evaluating the phonon Green's function via self-consistent diagrammatic perturbation theory. Our predicted phonon lifetimes at $T=600$ K agree well with our inelastic neutron scattering measurements across the entire Brillouin zone, and our thermal conductivity predictions agree well with previous measurements. Both the changes due to thermal expansion and self-consistent contributions are nontrivial at high temperatures, though the effects tend to cancel, and interband transitions yield a substantial contribution.

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arXiv2024

First-principles determination of the phonon-point defect scattering and thermal transport due to fission products in ThO2

This work presents the first principles calculations of the lattice thermal conductivity degradation due to point defects in thorium dioxide using an alternative solution of the Pierels-Boltzmann transport equation. We have used the non-perturbative Green's function methodology to compute the phonon point defect scattering rates that consider the local distortion around the point defect, including the mass difference changes, interatomic force constants and structural relaxation near the point defects. The point defects considered in the work include the vacancy of thorium and oxygen, substitution of helium, krypton, zirconium, iodine, xenon, in the thorium site, and the three different configuration of the Schottky defects. The results of the phonon-defect scattering rate reveals that among the considered intrinsic defects, the thorium vacancy and helium substitution in the thorium site scatter the phonon most due to substantial changes in the force constant and structural distortions. The scattering of phonons due to the substitutional defects unveils that the zirconium atom scatters phonons the least, followed by xenon, iodine, krypton, and helium. This is contrary to the intuition that the scattering strength follows HeTh > KrTh > ZrTh > ITh > XeTh based on the mass difference. This striking difference in the zirconium phonon scattering is due to the local chemical environment changes. Zirconium is an electropositive element with valency similar to thorium and, therefore, can bond with the oxygen atoms, thus creating less force constant variance compared to iodine, an electronegative element, noble gas helium, xenon, and krypton. These results can serve as the benchmark for the analytical models and help the engineering-scale modeling effort for nuclear design.

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arXiv2023

Anharmonic phonon behavior via irreducible derivatives: self-consistent perturbation theory and molecular dynamics

Cubic phonon interactions are now regularly computed from first principles, and the quartic interactions have begun to receive more attention. Given this realistic anharmonic vibrational Hamiltonian, the classical phonon Green's function can be precisely measured using molecular dynamics, which can then be used to rigorously assess the range of validity for self-consistent diagrammatic approaches in the classical limit. Here we use the bundled irreducible derivative approach to efficiently and precisely compute the cubic and quartic phonon interactions of CaF$_2$, systematically obtaining the vibrational Hamiltonian purely in terms of irreducible derivatives. non frequency shifts and linewidths, We demonstrate that the 4-phonon sunset diagram has an important contribution to the optical phonon linewidths beyond $T=500$ K. Reasonable results are obtained even at $T=900$ K when performing self-consistency using the 4-phonon loop diagram and evaluating the 3-phonon bubble and 4-phonon sunset diagrams post self-consistency. Further improvements are obtained by performing quasiparticle perturbation theory, where both the 4-phonon loop and the real part of the 3-phonon bubble are employed during self-consistency. Our irreducible derivative approach to self-consistent perturbation theory is a robust tool for studying anharmonic phonons in both the quantum and classical regimes.

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arXiv2023

Precise ground state of multi-orbital Mott systems via the variational discrete action theory

Determining the ground state of multi-orbital Hubbard models is critical for understanding strongly correlated electron materials, yet existing methods struggle to simultaneously reach zero temperature and infinite system size. The \textit{de facto} standard is to approximate a finite dimension multi-orbital Hubbard model with a $d=\infty$ version, which can then be formally solved via the dynamical mean-field theory (DMFT), though the DMFT solution is limited by the state of unbiased impurity solvers for zero temperature and multiple orbitals. The recently developed variational discrete action theory (VDAT) offers a new approach to solve the $d=\infty$ Hubbard model, with a variational ansatz that is controlled by an integer $\mathcal{N}$, and monotonically approaches the exact solution at an increasing computational cost. Here we propose a decoupled minimization algorithm to implement VDAT for the multi-orbital Hubbard model in $d=\infty$ and study $\mathcal{N}=2-4$ . At $\mathcal{N}=2$, VDAT rigorously recovers the multi-orbital Gutzwiller approximation, reproducing known results. At $\mathcal{N}=3$, VDAT precisely captures the competition between the Hubbard $U$, Hund $J$, and crystal field $Δ$ in the two orbital Hubbard model over all parameter space, with a negligible computational cost. For sufficiently large $U/t$ and $J/U$, we show that $Δ$ drives a first-order transition within the Mott insulating regime. In the large orbital polarization limit with finite $J/U$, we find that interactions have a nontrivial effect even for small $U/t$. VDAT will have far ranging implications for understanding multi-orbital model Hamiltonians and strongly correlated electron materials.

cond-mat.str-el↗

arXiv2023

A gauge constrained algorithm of VDAT at $\mathcal{N}=3$ for the multi-orbital Hubbard model

The recently developed variational discrete action theory (VDAT) provides a systematic variational approach to the ground state of the quantum many-body problem, where the quality of the solution is controlled by an integer $\mathcal{N}$, and increasing $\mathcal{N}$ monotonically approaches the exact solution. VDAT can be exactly evaluated in the $d=\infty$ multi-orbital Hubbard model using the self-consistent canonical discrete action theory (SCDA), which requires a self-consistency condition for the integer time Green's functions. Previous work demonstrates that $\mathcal{N}=3$ accurately captures multi-orbital Mott/Hund physics at a cost similar to the Gutzwiller approximation. Here we employ a gauge constraint to automatically satisfy the self-consistency condition of the SCDA at $\mathcal{N}=3$, yielding an even more efficient algorithm with enhanced numerical stability. We derive closed form expressions of the gauge constrained algorithm for the multi-orbital Hubbard model with general density-density interactions, allowing VDAT at $\mathcal{N}=3$ to be straightforwardly applied to the seven orbital Hubbard model. We present results and a performance analysis using $\mathcal{N}=2$ and $\mathcal{N}=3$ for the $\textrm{SU}(2\textrm{N}_{\textrm{orb}})$ Hubbard model in $d=\infty$ with $\textrm{N}_{\textrm{orb}}=2-8$, and compare to numerically exact dynamical mean-field theory solutions where available. The developments in this work will greatly facilitate the application of VDAT at $\mathcal{N}=3$ to strongly correlated electron materials.

cond-mat.str-el↗

arXiv2023

Magnetism and Metallicity in Moiré Transition Metal Dichalcogenides

The ability to control the properties of twisted bilayer transition metal dichalcogenides in situ makes them an ideal platform for investigating the interplay of strong correlations and geometric frustration. Of particular interest are the low energy scales, which make it possible to experimentally access both temperature and magnetic fields that are of the order of the bandwidth or the correlation scale. In this manuscript we analyze the moiré Hubbard model, believed to describe the low energy physics of an important subclass of the twisted bilayer compounds. We establish its magnetic and the metal-insulator phase diagram for the full range of magnetic fields up to the fully spin polarized state. We find a rich phase diagram including fully and partially polarized insulating and metallic phases of which we determine the interplay of magnetic order, Zeeman-field, and metallicity, and make connection to recent experiments.

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arXiv2023

Foundations of the Variational Discrete Action Theory

Variational wave functions and Green's functions are two important paradigms for solving quantum Hamiltonians, each having their own advantages. Here we detail the Variational Discrete Action Theory (VDAT), which exploits the advantages of both paradigms in order to approximately solve the ground state of quantum Hamiltonians. VDAT consists of two central components: the sequential product density matrix (SPD) ansatz and a discrete action associated with the SPD. The SPD is a variational ansatz inspired by the Trotter decomposition and characterized by an integer $\mathcal{N}$, recovering many well known variational wave functions, in addition to the exact solution for $\mathcal{N}=\infty$. The discrete action describes all dynamical information of an effective integer time evolution with respect to the SPD. We generalize the path integral to our integer time formalism, which converts a dynamic correlation function in integer time to a static correlation function in a compound space. We also generalize the usual many-body Green's function formalism to integer time, which results in analogous but distinct mathematical structures, yielding integer time versions of the generating functional, Dyson equation, and Bethe-Salpeter equation. We prove that the SPD can be exactly evaluated in the multi-band Anderson impurity model (AIM) by summing a finite number of diagrams. For the multi-band Hubbard model, we prove that the self-consistent canonical discrete action approximation (SCDA), which is the integer time analogue of the dynamical mean-field theory, exactly evaluates the SPD for $d=\infty$. VDAT within the SCDA provides an efficient yet reliable method for capturing the local physics of quantum lattice models, which will have broad applications for strongly correlated electron materials. More generally, VDAT should find applications in various many-body problems in physics.

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arXiv2022

Capturing the ground state of uranium dioxide from first principles: crystal distortion, magnetic structure, and phonons

Uranium dioxide (UO$_2$) remains a formidable challenge for first-principles approaches, due to the complex interplay among spin-orbit coupling, Mott physics, magnetic ordering, and crystal distortions. Here we use DFT+$U$ to explore UO$_2$ at zero temperature, incorporating all the aforementioned phenomena. The technical challenge is to navigate the many metastable electronic states produced by DFT+$U$, which is acomplished using $f$-orbital occupation matrix control to search for the ground state. We restrict our search to the high-symmetry ferromagnetic phase, including spin-orbit coupling, which produces a previously unreported occupation matrix. This newfound occupation matrix is then used as an initialization to explore the broken symmetry phases. We find the oxygen cage distortion of the 3k antiferromagnetic state to be in excellent agreement with experiments, and both the spin-orbit coupling and the Hubbard $U$ are critical ingredients. We demonstrate that only select phonon modes have a strong dependence on the Hubbard $U$, whereas magnetic ordering has only a small influence overall. We perform measurements of the phonon dispersion curves using inelastic neutron scattering, and our calculations show good agreement when using reasonable values of $U$. The quantitative success of DFT+$U$ warrants exploration of thermal transport and other observables within this level of theory.

cond-mat.mtrl-sci↗

arXiv2022

Thermal Energy Transport in Oxide Nuclear Fuel

To efficiently capture the energy of the nuclear bond, advanced nuclear reactor concepts seek solid fuels that must withstand unprecedented temperature and radiation extremes. In these advanced fuels, thermal energy transport under irradiation is directly related to reactor performance as well as reactor safety. The science of thermal transport in nuclear fuel is a grand challenge due to both computational and experimental complexities. Here, we provide a comprehensive review of thermal transport research on two actinide oxides: one currently in use in commercial nuclear reactors, uranium dioxide (UO2), and one advanced fuel candidate material, thorium dioxide (ThO2). In both materials, heat is carried by lattice waves or phonons. Crystalline defects caused by fission events effectively scatter phonons and lead to a degradation in fuel performance over time. Bolstered by new computational and experimental tools, researchers are now developing the foundational work necessary to accurately model and ultimately control thermal transport in advanced nuclear fuel. We begin by reviewing research aimed at understanding thermal transport in perfect single crystals. The absence of defects enables studies that focus on the fundamental aspects of phonon transport. Next, we review research that targets defect generation and evolution. Here, the focus is on ion irradiation studies used as surrogates for damage caused by fission products. We end this review with a discussion of modeling and experimental efforts directed at predicting and validating mesoscale thermal transport in the presence of irradiation defects. While efforts into these research areas have been robust, challenging work remains in developing holistic tools to capture and predict thermal energy transport across widely varying environmental conditions.

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arXiv2022

The generalized quasiharmonic approximation via space group irreducible derivatives

The quasiharmonic approximation (QHA) is the simplest nontrivial approximation for interacting phonons under constant pressure, bringing the effects of anharmonicity into temperature dependent observables. Nonetheless, the QHA is often implemented with additional approximations due to the complexity of computing phonons under arbitrary strains, and the generalized QHA, which employs constant stress boundary conditions, has not been completely developed. Here we formulate the generalized QHA, providing a practical algorithm for computing the strain state and other observables as a function of temperature and true stress. We circumvent the complexity of computing phonons under arbitrary strains by employing irreducible second order displacement derivatives of the Born-Oppenheimer potential and their strain dependence, which are efficiently and precisely computed using the lone irreducible derivative approach. We formulate two complementary strain parametrizations: a discretized strain grid interpolation and a Taylor series expansion in symmetrized strain. We illustrate our approach by evaluating the temperature and pressure dependence of the elastic constant tensor and the thermal expansion in thoria (ThO$_2$) using density functional theory with three exchange-correlation functionals. The QHA results are compared to our measurements of the elastic constant tensor using time domain Brillouin scattering and inelastic neutron scattering. Our irreducible derivative approach simplifies the implementation of the generalized QHA, which will facilitate reproducible, data driven applications.

cond-mat.mtrl-sci↗

arXiv2022

Validating First-Principles Phonon Lifetimes via Inelastic Neutron Scattering

Phonon lifetimes are a key component of quasiparticle theories of transport, yet first-principles lifetimes are rarely directly compared to inelastic neutron scattering (INS) results. Existing comparisons show discrepancies even at temperatures where perturbation theory is expected to be reliable. In this work, we demonstrate that the reciprocal space voxel ($q$-voxel), which is the finite region in reciprocal space required in INS data analysis, must be explicitly accounted for within theory in order to draw a meaningful comparison. We demonstrate accurate predictions of peak widths of the scattering function when accounting for the $q$-voxel in CaF$_2$ and ThO$_2$. Passing this test implies high fidelity of the phonon interactions and the approximations used to compute the Green's function, serving as critical benchmark of theory, and indicating that other material properties should be accurately predicted; which we demonstrate for thermal conductivity.

cond-mat.mtrl-sci↗

arXiv2020

Variational Discrete Action Theory

Here we propose the Variational Discrete Action Theory (VDAT) to study the ground state properties of quantum many-body Hamiltonians. VDAT is a variational theory based on the sequential product density matrix (SPD) ansatz, characterized by an integer $\mathcal{N}$, which monotonically approaches the exact solution with increasing $\mathcal{N}$. To evaluate the SPD, we introduce a discrete action and a corresponding integer time Green's function. We use VDAT to exactly evaluate the SPD in two canonical models of interacting electrons: the Anderson impurity model (AIM) and the $d=\infty$ Hubbard model. For the latter, we evaluate $\mathcal{N}=2-4$, where $\mathcal{N}=2$ recovers the Gutzwiller approximation (GA), and we show that $\mathcal{N}=3$, which exactly evaluates the Gutzwiller-Baeriswyl wave function, provides a truly minimal yet precise description of Mott physics with a cost similar to the GA. VDAT is a flexible theory for studying quantum Hamiltonians, competing both with state-of-the-art methods and simple, efficient approaches all within a single framework.

cond-mat.str-el↗

arXiv2020

Compositional phase stability of correlated electron materials within DFT+DMFT

Predicting the compositional phase stability of strongly correlated electron materials is an outstanding challenge in condensed matter physics, requiring precise computations of total energies. In this work, we employ the density functional theory plus dynamical mean-field theory (DFT+DMFT) formalism to address local correlations due to transition metal d electrons on compositional phase stability in the prototype rechargeable battery cathode material LixCoO2, and detailed comparisons are made with the simpler DFT+U approach (i.e. the Hartree-Fock solution of the DMFT impurity problem). Local interactions are found to strongly impact the energetics of the band insulator LiCoO2, most significantly via the Eg orbitals, which are partially occupied via hybridization with O p states. We find CoO2 and Li1/2CoO2 to be moderately correlated Fermi liquids with quasiparticle weights of 0.6-0.8 for the T2g states, which are most impacted by the interactions. As compared to DFT+U, DFT+DMFT considerably dampens the increase in total energy as U is increased, which indicates that dynamical correlations are important to describe this class of materials despite the relatively modest quasiparticle weights. Unlike DFT+U, which can incorrectly drive LixCoO2 towards spurious phase separating or charge ordered states, DFT+DMFT correctly captures the system's phase stability and does not exhibit a strong charge ordering tendency. Most importantly, the error within DFT+U varies strongly as the composition changes, challenging the common practice of artificially tuning U within DFT+U to compensate the errors of Hartree-Fock. DFT+DMFT predicts the average intercalation voltage decreases relative to DFT, opposite to the result of DFT+U, which would yield favorable agreement with experiment in conjunction with the overprediction of the voltage by the strongly constrained and appropriately normed DFT functional.

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