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All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Revealing short- and long-range Li-ion diffusion in Li 2 MnO 3 from finite-temperature dynamical mean field theory

Li 2 MnO 3 is a key component of Li-excess layered cathodes of the form (1 − x), LiMO 2 + x, Li 2 MnO 3 (M = Mn, Ni, Co, …), yet its role in setting Li-ion transport limitations remains under debate. Here, in this study, we combine DFT+U, finite-temperature DFT+DMFT with a continuous-time quantum Monte Carlo impurity solver, and nudged-elastic-band (NEB) calculations to study Li + migration in paramagnetic Li 2 MnO 3 in the presence of a single Li vacancy. Evaluating DMFT total energies along the DFT+U NEB geometries reveals that dynamical correlations strongly renormalize the lowest-barrier processes, reducing the activation energies to E a = 0.18 eV for the shortest-range hop and E a = 0.50 eV for the next-lowest (transport-controlling) step. The 0.18 eV barrier quantitatively reproduces the short-range activation energy from µ+SR, while the 0.50 eV barrier is consistent with the long-range transport scale extracted from ac-impedance measurements. This single-vacancy, paramagnetic DMFT description thus provides a unified interpretation of local and macroscopic probes without invoking clustered vacancy configurations or strong extrinsic disorder, consistent with nearly stoichiometric Li 2 MnO 3 powders. More broadly, our results highlight finite-temperature dynamical correlations as an essential ingredient for predicting ionic migration energetics in correlated oxide electrodes.

Lee, Alex Taekyung [University of Illinois, Chicag↗
DOE OSTI2025

DFT-based insight into finite-temperature properties of ferroelectric perovskites with lone-pair: the case of CsGeX 3 (X = Cl, Br, I)

Ferroelectrics remain in the focus of scientific attention for decades owing to their fundamental and practical appeal. Recently, ferroelectricity has been demonstrated in semiconducting halide perovskites (Zhang et al 2022 Sci. Adv. 8 eabj5881), offering both a rare combination of ferroelectricity and semiconductivity in the same material and a possible alternative to the prevailing perovskite oxide ferroelectrics. We propose a route to simulating such materials at finite temperatures capable of reproducing key experimental and first-principle data, such as Curie temperature, phase transition sequence, spontaneous polarization, and soft mode frequencies. The key methodological finding is the superior performance of hybrid exchange correlation functionals in parametrization of effective Hamiltonians for ferroelectrics with lone pair. The parametrization for effective Hamiltonians for CsGeX 3 (X = Cl, Br, I) is reported. The application of methodology to study polarization reversal in CsGeX 3 allows for the development of a ‘minimalistic’ model for polarization reversal in ferroelectrics that provides an insight into the mechanisms of polarization reversal and its key features, such as the relationship between the coercive field, temperature, and AC field frequency. Importantly, the model reveals the origin of the well-known and ever-puzzling overestimation of coercive fields in computations. Furthermore, we report a variety of finite-temperature properties of CsGeX 3 ferroelectrics, such as dielectric susceptibility, pyroelectric coefficients, and energy storage density, which reveal that these halide perovskites possess properties comparable to their oxide counterparts. Here, we believe that our work provides significant methodological advancements, deepens fundamental understanding of ferroelectrics, and reveals the potential of halide perovskite ferroelectrics.

effective Hamiltonian↗
DOE OSTI2025

Framework for phase transitions between the Maxwell and Gibbs constructions at finite temperature

The characteristics of the hadron-to-quark first-order phase transition differ depending on whether charge neutrality is locally or globally fulfilled. In 𝛽-equilibrated matter, these two possibilities correspond to the Maxwell and Gibbs constructions. Recently, we presented a new framework in which a continuously varying parameter allows one to describe a first-order phase transition in intermediate scenarios to the two extremes of fully local and fully global charge neutrality. In this work, we extend the previous framework to finite temperatures and out-of-𝛽 equilibrium conditions, making it available for simulations of core-collapse supernovae and binary neutron star mergers. We investigate its impact on key thermodynamic quantities across a range of baryon densities, temperatures, and electron fractions. We find that when matter is not in 𝛽 equilibrium, the pressure in the mixed phase is not constant even for the case of fully local charge neutrality. Moreover, we compute the thermal index using three different approaches, demonstrating that the finite-temperature extension of an equation of state using a constant thermal index can be ill defined when applied to the mixed phase.

QCD phase transitions↗
DOE OSTI2020

Finite-temperature many-body perturbation theory in the grand canonical ensemble

A finite-temperature many-body perturbation theory is presented, which expands in power series the electronic grand potential, chemical potential, internal energy, and entropy on an equal footing. Sum-over-states and sum-over-orbitals analytical formulas for the second-order perturbation corrections to these thermodynamic properties are obtained in a time-independent, nondiagrammatic, algebraic derivation, relying on the sum rules of the Hirschfelder–Certain degenerate perturbation energies in a degenerate subspace as well as nine algebraic identities for the zeroth-order thermal averages of one- through four-indexed quantities and products thereof. Lastly, they reproduce numerically exactly the benchmark data obtained as the numerical derivatives of the thermal-full-configuration-interaction results for a wide range of temperatures.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

A phaseless auxiliary-field quantum Monte Carlo perspective on the uniform electron gas at finite temperatures: Issues, observations, and benchmark study

We investigate the viability of the phaseless finite-temperature auxiliary-field quantum Monte Carlo (ph-FT-AFQMC) method for ab initio systems using the uniform electron gas as a model. Through comparisons with exact results and FT coupled cluster theory, we find that ph-FT-AFQMC is sufficiently accurate at high to intermediate electronic densities. We show, both analytically and numerically, that the phaseless constraint at FT is fundamentally different from its zero-temperature counterpart (i.e., ph-ZT-AFQMC), and generally, one should not expect ph-FT-AFQMC to agree with ph-ZT-AFQMC in the low-temperature limit. With an efficient implementation, we are able to compare exchange-correlation energies to the existing results in the thermodynamic limit and find that the existing parameterizations are highly accurate. In particular, we found that ph-FT-AFQMC exchange-correlation energies are in better agreement with a known parameterization than is restricted path-integral MC in the regime of Θ ≤ 0.5 and rs ≤ 2, which highlights the strength of ph-FT-AFQMC.

Lee, Joonho (ORCID:0000000296671081)↗
DOE OSTI2025

Exotic phases in finite-density ℤ 3 theories

Lattice ℤ 3 theories with complex actions share many key features with finite- density QCD including a sign problem and $\mathcal{CK}$ symmetry. Complex ℤ 3 spin and gauge models exhibit a generalized Kramers-Wannier duality mapping them onto chiral ℤ 3 spin and gauge models, which are simulatable with standard lattice methods in large regions of parameter space. The Migdal-Kadanoff real-space renormalization group (RG) preserves this duality, and we use it to compute the approximate phase diagram of both spin and gauge ℤ 3 models in dimensions one through four. Chiral ℤ 3 spin models are known to exhibit a Devil’s Flower phase structure, with inhomogeneous phases that can be thought of as ℤ 3 analogues of chiral spirals. Out of the large class of models we study, we find that only chiral spin models and their duals have a Devil’s Flower structure with an infinite set of inhomogeneous phases, a result we attribute to Elitzur’s theorem. We also find that different forms of the Migdal-Kadanoff RG produce different numbers of phases, a violation of the expectation for universal behavior from a real-space RG. We discuss extensions of our work to ℤ N models, SU(N) models and nonzero temperature.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Real-Frequency Response Functions at Finite Temperature

Building on previous developments [A. Taheridehkordi, S. H. Curnoe, and J. P. F. LeBlanc, Phys. Rev. B 99, 035120 (2019); A. Taheridehkordi, S. H. Curnoe, and J. P. F. LeBlancPhys. Rev. B101, 125109 (2020); A. Taheridehkordi, S. H. Curnoe, and J. P. F. LeBlancPhys. Rev. B102, 045115 (2020), B. Holm and U. von Barth, Phys. Rev. B 57, 2108 (1998), J. Vičičevic and M. Ferrero, Phys. Rev. B 101, 075113 (2020)], we show that the diagrammatic Monte Carlo technique allows us to compute finite-temperature response functions directly on the real-frequency axis within any field-theoretical formulation of the interacting fermion problem. There are no limitations on the type and nature of the system’s action or whether partial summation and self-consistent treatment of certain diagram classes are used. In particular, by eliminating the need for numerical analytic continuation from a Matsubara representation, our scheme allows us to study spectral densities of arbitrary complexity with controlled accuracy in models with frequency-dependent effective interactions. Finally, for illustrative purposes we consider the problem of the plasmon linewidth in a homogeneous electron gas (jellium).

3-dimensional systems↗
DOE OSTI2025

Pauli potential formalism at finite temperature

At zero temperature, the Pauli potential—the functional derivative of the Pauli kinetic energy density functional—is the key to the accuracy of the orbital-free density functional theory (OFDFT) as it is supposed to capture all the effects associated with the Pauli exclusion principle. Here, we extend this concept to finite temperature by defining Pauli free energy and the modified Pauli free energy, both representing the natural generalizations of the Pauli term from zero- T to finite- T . We discuss their physical interpretation, the mathematical nuances, and the applicability, arguing that the modified Pauli potential should be used as an extension of the zero- T counterpart within the OF-DFT framework. Through analytical and numerical methods, we then analyze some of the exact properties concerning the modified Pauli free- and kinetic-energy terms and examine the temperature dependence of the modified Pauli potential.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Accelerating Finite-temperature Kohn-Sham Density Functional Theory\ with Deep Neural Networks

We present a numerical modeling workflow based on machine learning (ML) which reproduces the the total energies produced by Kohn-Sham density functional theory (DFT) at finite electronic temperature to within chemical accuracy at negligible computational cost. Based on deep neural networks, our workflow yields the local density of states (LDOS) for a given atomic configuration. From the LDOS, spatially-resolved, energy-resolved, and integrated quantities can be calculated, including the DFT total free energy, which serves as the Born-Oppenheimer potential energy surface for the atoms. We demonstrate the efficacy of this approach for both solid and liquid metals and compare results between independent and unified machine-learning models for solid and liquid aluminum. Our machine-learning density functional theory framework opens up the path towards multiscale materials modeling for matter under ambient and extreme conditions at a computational scale and cost that is unattainable with current algorithms.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Accelerating Finite-Temperature Kohn-Sham Density Functional Theory with Deep Neural Networks

We present a numerical modeling workflow based on machine learning (ML) which reproduces the total energies produced by Kohn-Sham density functional theory (DFT) at finite electronic temperature to within chemical accuracy at negligible computational cost. Based on deep neural networks, our workflow yields the local density of states (LDOS) for a given atomic configuration. From the LDOS, spatially-resolved, energy-resolved, and integrated quantities can be calculated, including the DFT total free energy, which serves as the Born-Oppenheimer potential energy surface for the atoms. We demonstrate the efficacy of this approach for both solid and liquid metals and compare results between independent and unified machine-learning models for solid and liquid aluminum. Our machine-learning density functional theory framework opens up the path towards multiscale materials modeling for matter under ambient and extreme conditions at a computational scale and cost that is unattainable with current algorithms.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Momentum distribution of the uniform electron gas at finite temperature: Effects of spin polarization

We carry out extensive direct path integral Monte Carlo (PIMC) simulations of the uniform electron gas (UEG) at finite temperature for different values of the spin-polarization ξ. This allows us to unambiguously quantify the impact of spin effects on the momentum distribution function n(k) and related properties. We find that interesting physical effects like the interaction-induced increase in the occupation of the zero-momentum state n(0) substantially depend on ξ. Our results further advance the current understanding of the UEG as a fundamental model system, and are of practical relevance for the description of transport properties of warm dense matter in an external magnetic field. All PIMC results are freely available online and can be used as a benchmark for the development of methods and applications.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Tensor network study of the m = 1/2 magnetization plateau in the Shastry-Sutherland model at finite temperature

The two-dimensional infinite projected entangled pair state tensor network is evolved in imaginary time with the full update (FU) algorithm to simulate the Shastry-Sutherland model in a magnetic field at finite temperature directly in the thermodynamic limit. We focus on the phase transition into the m = 1/2 magnetization plateau, which was observed in experiments on SrCu 2 (BO 3 ) 2 . For the largest simulated bond dimension, the early evolution in the high-temperature regime is simulated with the simple update (SU) scheme and then, as the correlation length increases, continued with the FU scheme towards the critical regime. We apply a small symmetry-breaking bias field and then extrapolate towards zero bias using a simple scaling theory in the bias field. The combined SU + FU scheme provides an accurate estimate of the critical temperature, even though the results could not be fully converged in the bond dimension in the vicinity of the transition. Here, the critical temperature estimate is improved with a generalized scaling theory that combines two divergent length scales: One due to the bias, and the other due to the finite bond dimension. The obtained results are consistent with the transition being in the universality class of the two-dimensional classical Ising model. The estimated critical temperature is 3.5(2) K, which is well above the temperature 2.1 K used in the experiments.

2-dimensional systems↗
DOE OSTI2024

Removing Basis Set Incompleteness Error in Finite-Temperature Electronic Structure Calculations: Two-Electron Systems

We investigate the basis-set-size dependence for quantities related to interacting electrons in the canonical ensemble. Calculations are performed using exact diagonalization (finite temperature full configuration interaction method) on two-electron model systems–the uniform electron gas (UEG) and the helium atom. Our data reproduce previous observations of a competition for how the internal energy converges between the ground-state correlation energy and the high-temperature kinetic energy. We explore how this can be related to component parts of the internal energy including kinetic, exchange, and correlation energies and show there is surprising nuance in how this can be broken down into mostly monotonically converging quantities. We also show that separation of the free energy into a free energy with/without correlation allows for monotonic convergence with basis set size due to the variational principle. We find that the free energy convergence matches the previously observed convergence properties of the internal energy. We discuss the free energy divergence that happens when converging a finite basis analytical hydrogen atom to the complete basis set limit and compare this to the energies of a helium atom in a large periodic box. Reducing the box size, we saw convergence trends for the helium atom that were similar to the UEG.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Intertwined States at Finite Temperatures in the Hubbard Model

We report significant advances in numerical techniques have enabled recent breakthroughs in the study of various properties of the Hubbard model - a seemingly simple, yet complex model of correlated electrons that has been a focus of study for more than half a century. In particular, it captures the essence of strong correlations, and is believed to possess various emergent, low energy states and collective excitations characteristic of cuprate high-temperature superconducting materials. While a thorough review of all activity is not possible here, we have focused the discussion on our recent work using unbiased, numerically exact, “brute force”, finite temperature quantum Monte Carlo methods. Our various studies reveal a rich variety of quantum liquid crystal phases, and complementary transport properties, which answer some questions, but certainly raise others concerning “strange metal” behavior and the ultimate fate of quasiparticles in the Hubbard model.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Paradigm for approaching the forbidden phase transition in the one-dimensional Ising model at fixed finite temperature: Single chain in a magnetic field

In a previous paper, the forbidden spontaneous phase transition in the one-dimensional Ising model was found to be approachable arbitrarily closely in decorated ladders by ultra-narrow phase crossover (UNPC) at a given finite temperature T 0 with the crossover width 2δT reduced exponentially, which resemble a genuine first-order transition with large latent heat. Here, I reveal that the forbidden phase transition can be approached at fixed T 0 as well in decorated single-chain Ising models in the presence of a magnetic field, in which T 0 is determined by the interactions involving only the decorated parts and the magnetic field, while 2δT is independently, exponentially reduced (δT = 0 means a genuine transition) by restoring the ferromagnetic interaction between the ordinary spins on the chain backbone-which was neglected in the previous studies of pseudo-transition-thus manifesting that this asymptoticity to the forbidden transition is essentially the buildup of coherence in preformed crossover of local states. Furthermore, I show that the UNPC can be realized even in the absence of the conventional geometric frustration because the magnetic field itself can induce previously unnoticed hidden spin frustration. In conclusion, these findings make the doors wide open to the engineering and utilization of UNPC as a new paradigm for exploring exotic phenomena and 1D device applications.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

The coupled SYK model at finite temperature

Sachdev-Ye-Kitaev (SYK) model, which describes N randomly interacting Majorana fermions in 0+1 dimension, is found to be an solvable UV-complete toy model for holographic duality in nearly AdS 2 dilaton gravity. Ref. [1] proposed a modified model by coupling two identical SYK models, which at low-energy limit is dual to a global AdS 2 geometry. This geometry is an “eternal wormhole" because the two boundaries are causally connected. Increasing the temperature drives a Hawking-Page like transition from the eternal wormhole geometry to two disconnected black holes with coupled matter field. To gain more understanding of the coupled SYK model, in this work, we study the finite temperature spectral function of this system by numerical solving the Schwinger-Dyson equation in real-time. We find in the low-temperature phase the system is well described by weakly interacting fermions with renormalized single-particle gap, while in the high temperature phase the system is strongly interacting and the single-particle peaks merge. We also study the q dependence of the spectral function.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1992

Entropic uncertainty relation at finite temperature

We discussed how much information is lost when a particle is in equilibrium with the thermal reservoir of temperature T = 1/beta. The universal temperature correction to the r.h.s. of U(X,P:psi) greater than or = 1 + ln(pi) is determined. For this purpose, it is convenient to employ the framework of thermo-field dynamics (TFD). This formulation of finite-temperature (T not = 0) quantum theory utilizes the doubled Hilbert space, the normal operator (A) acting on the objective space, and its corresponding tildian operator on the fictitious space. The physical probability density associated with the measurement of the normal operator, A, is given, and the information entropy at T not = 0 is defined. The results describe how the thermal disturbance effects in S sub X or S sub P (delta X or delta P) can be suppressed by squeezing with keeping U = S sub X + S sub P (delta X x delta P) its minimum value.

Abe, Sumiyoshi↗