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All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Quantum solver for single-impurity Anderson models with particle-hole symmetry

Quantum embedding methods, such as dynamical mean-field theory (DMFT), provide a powerful framework for investigating strongly correlated materials. A central computational bottleneck in DMFT is in solving the Anderson impurity model (AIM), whose exact solution is classically intractable for large bath sizes. In this work, we benchmark a quantum-classical hybrid solver tailored for particle-hole symmetric AIMs, using the variational quantum eigensolver to prepare the ground state of the model with shallow quantum circuits. The solver uses shallow quantum ansätze and one set of variational parameters to prepare the ground state and its particle and hole excitations, enabling the construction of the impurity Green’s function through a continued-fraction expansion. We evaluate the performance of this approach across a few bath sizes and interaction strengths under noisy, shot-limited conditions. We compare three optimization routines (COBYLA, Adam, and L-BFGS-B) in terms of convergence and fidelity, assess the benefits of estimating a quantum-computed moment correction to the variational energies, and benchmark the approach by comparing the density of states computed from the impurity Green’s function against that obtained using a classical pipeline. Our results demonstrate the feasibility of Green’s function construction on near-term devices and establish practical benchmarks for quantum impurity solvers embedded within self-consistent DMFT loops.

Karabin, Mariia [ORNL]↗
DOE OSTI2022

Interaction-expansion inchworm Monte Carlo solver for lattice and impurity models

Multiorbital quantum impurity models with general interaction and hybridization terms appear in a wide range of applications, including embedding, quantum transport, and nanoscience. However, most quantum impurity solvers are restricted to a few impurity orbitals, discretized baths, diagonal hybridizations, or density-density interactions. We generalize the inchworm quantum Monte Carlo method to the interaction expansion, and we explore its application to typical single- and multiorbital problems encountered in investigations of impurity and lattice models. Our implementation generically outperforms bare and bold-line quantum Monte Carlo algorithms in the interaction expansion. For the systems studied here, our implementation remains inferior to the more specialized hybridization expansion and auxiliary field algorithms. So, the problem of convergence to unphysical fixed points, which hampers so-called bold-line methods, is not encountered in inchworm Monte Carlo.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Tensor train continuous time solver for quantum impurity models

The simulation of strongly correlated quantum impurity models is a significant challenge in modern condensed matter physics that has multiple important applications. Thus far, the most successful methods for approaching this challenge involve Monte Carlo techniques that accurately and reliably sample perturbative expansions to any order. However, the cost of obtaining high precision through these methods is high. Recently, tensor train decomposition techniques have been developed as an alternative to Monte Carlo integration. In this study, we apply these techniques to the single-impurity Anderson model at equilibrium by calculating the systematic expansion in power of the hybridization of the impurity with the bath. Furthermore, we demonstrate the performance of the method in a paradigmatic application, examining the first-order phase transition on the infinite-dimensional Bethe lattice, which can be mapped to an impurity model through dynamical mean field theory. Our results indicate that using tensor train decomposition schemes allows the calculation of finite-temperature Green's functions and thermodynamic observables with unprecedented accuracy. The methodology holds promise for future applications to frustrated multiorbital systems, using a combination of partially summed series with other techniques pioneered in diagrammatic and continuous time quantum Monte Carlo.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Mechanism of superconductivity in the Hubbard model at intermediate interaction strength

We study the fluctuations responsible for pairing in the d -wave superconducting state of the two-dimensional Hubbard model at intermediate coupling within a cluster dynamical mean-field theory with a numerically exact quantum impurity solver. By analyzing how momentum- and frequency-dependent fluctuations generate the d -wave superconducting state in different representations, we identify antiferromagnetic fluctuations as the pairing glue of superconductivity in both the underdoped and the overdoped regime. Nevertheless, in the intermediate coupling regime, the predominant magnetic fluctuations may differ significantly from those described by conventional spin fluctuation theory.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Neural Network Solver for Small Quantum Clusters

Machine learning approaches have recently been applied to the study of various problems in physics. Most of these studies are focused on interpreting the data generated by conventional numerical methods or the data on an existing experimental database. An interesting question is whether it is possible to use a machine learning approach, in particular a neural network, for solving the many-body problem. In this paper, we present a neural network solver for the single impurity Anderson model, the paradigm of an interacting quantum problem in small clusters. We demonstrate that the neural-network-based solver provides quantitative accurate results for the spectral function as compared to the exact diagonalization method. This opens the possibility of utilizing the neural network approach as an impurity solver for other many-body numerical approaches, such as the dynamical mean field theory.

36 MATERIALS SCIENCE↗
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 OSTI2023

Delocalized polaron and Burstein-Moss shift induced by Li in α–V 2 O 5 : A DFT + DMFT study

For this work, we performed density functional theory (DFT)+U and dynamical mean field theory (DMFT) calculations with a continuous-time quantum Monte Carlo impurity solver to investigate the electronic properties of V 2 O 5 and Li x V 2 O 5 (x = 0.125 and 0.25). Pristine V 2 O 5 is a charge-transfer insulator with strong O p–V d hybridization, and it exhibits a large band gap (E gap ) as well as a nonzero conduction-band (CB) gap.We show that the band gap, the number of d electrons of vanadium, N d , and the CB gap for V 2 O 5 obtained from our DMFT calculations are in excellent agreement with the experimental values. While the DFT +U approach replicates the experimental band gap, it overestimates the value of N d and underestimates the CB gap. In the presence of low Li doping, the electronic properties of V 2 O 5 are mainly driven by a polaronic mechanism, and electron spin resonance and electron nuclear double resonance spectroscopies observed the coexistence of free and bound polarons. Notably, our DMFT results identify both polaron types, with the bound polaron being energetically preferred, while the DFT +U method only predicts the free polaron. Our DMFT analysis also reveals that increased Li doping leads to electron filling in the conduction band, shifting the Fermi level. This result is consistent with the observed Burstein-Moss shift upon enhanced Li doping, and we thus demonstrate that the DFT + DMFT approach can be used for an accurate and realistic description of strongly correlated materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Effect of off-diagonal elements in the Wannier Hamiltonian on DFT + DMFT for low-symmetry materials: Study of Li 2 MnO 3

Here, we study the effect of the off-diagonal elements of the Wannier Hamiltonian on the electronic structure of the low-symmetry material Li 2 MnO 3 ( C2/m ), using dynamical mean field theory calculations with a continuous-time quantum Monte Carlo impurity solver. The presence of significant off-diagonal elements leads to a pronounced suppression of the energy gap. The off-diagonal elements are largest when the Wannier projection is used based on the global coordinate, and they remain substantial even with the projection using the local coordinate close to the direction of Mn-O bonds. We show that the energy gap is enhanced by the diagonalization of the Mn d block in the full p-d Hamiltonian with the application of a unitary rotation matrix. Additionally, the inclusion of small double counting energy is crucial for achieving the experimental gap by reducing p-d hybridization. Furthermore, we establish the efficiency of a low-energy (d-only basis) model for studying the electronic structure of Li 2 MnO 3 , as the Wannier basis represents a hybridized state of Mn d and O p orbitals. These findings suggest an appropriate approach for investigating low-symmetry materials using the density functional theory plus dynamical mean field theory (DFT + DMFT) method. We also find that the antiferromagnetic ground state $\Gamma$ 2u is stable with U ≤ 2 eV within density functional theory+$U$ calculations, which is much smaller than the widely used U = 5 eV.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2026

Optimization performance, fidelity, and cost: SIAM VQE

This dataset contains files storing results from classically-simulated quantum subroutines within a dynamical mean-field theory workflow, and jupyter notebooks processing the data in these files to generate plots. The files store: (1) Results from variational quantum eigensolver (VQE) simulations searching for optimal parameters allowing parametrized quantum circuits to prepare approximations to ground states of different Anderson impurity models (AIMs) (2) Results from simulations of a quantum Lanczos algorithm (QLA) estimating the Lanczos coefficients defining the continued-fraction representation of an (AIM) Green’s function Description: Any file named vqe_gs_results* stores approximations to the ground state and energy of a given AIM estimated using three different methods: (1) Numerical diagonalization (2) Ideal VQE simulation (3) VQE simulation with sampling noise For each VQE simulations metadata about the optimization (optimization results plus number of quantum circuits that would have been executed on real hardware) is also stored. Any file named qla_dos_results* estimations for the Lanczos coefficients defining the Green’s function of an AIM. The stored estimations are achieved using different methods: (1) Numerical Lanczos algorithm from initial states obtained from numerical diagonalization (2) Simulated quantum Lanczos algorithm from initial states prepared from parametrized quantum circuits yielded by corresponding ideal and noisy VQE subroutines. The dataset is used and described in M. Karabin et al., "Quantum solver for single-impurity Anderson models with particle-hole symmetry", Phys. Rev. Research 8, 033066 (2026). DOI: https://doi.org/10.1103/7ys3-tl4l

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Is the Orbital-Selective Mott Phase Stable against Interorbital Hopping?

The localization-delocalization transition is at the heart of strong correlation physics. Recently, there is great interest in multiorbital systems where this transition can be restricted to certain orbitals, leading to an orbital-selective Mott phase (OSMP). Theoretically, the OSMP is widely studied for kinetically decoupled orbitals, but the effect of interorbital hopping remains unclear. Here, we show how nonlocal interorbital hopping leads to local hybridization in single-site dynamical mean-field theory (DMFT). Under fairly general circumstances, this implies that, at zero temperature, the OSMP, involving the Mott-insulating state of one orbital, is unstable against interorbital hopping to a different, metallic orbital. We further show that the coherence scale below which all electrons are itinerant is very small and gets exponentially suppressed even if the interorbital hopping is not overly small. Within this framework, the OSMP with interorbital hopping may thus reach down to extremely low temperatures T, but not to T = 0. Accordingly, it is part of a coherence-incoherence crossover and not a quantum critical point. Finally, we present analytical arguments supported by numerical results using the numerical renormalization group as a DMFT impurity solver. We also compare our findings with previous slave-spin studies.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Fault-tolerant operation and materials science with neutral atom logical qubits

We report on the fault-tolerant operation of logical qubits on a neutral atom quantum computer, with logical performance surpassing physical performance for multiple circuits including Bell state preparation (12x error reduction), random circuits (15x), and a prototype Anderson Impurity Model ground state solver for materials science applications (up to 6x, non-fault-tolerantly). The logical qubits are implemented via the [[4, 2, 2]] code (C 4 ). Our work constitutes the first complete realization of the benchmarking protocol proposed by Gottesman 2016 demonstrating results consistent with fault tolerance. In light of recent advances on applying concatenated C 4 /C 6 detection codes to achieve error correction with high code rates and thresholds, our work can be regarded as a building block towards a practical scheme for fault tolerant quantum computation. Our demonstration of a materials science application with logical qubits particularly demonstrates the immediate value of these techniques on current experiments.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Flat-band driven Kondo breakdown and reentrant effects in heavy-fermion moiré superlattices

Moiré superlattices (MSLs) in van der Waals heterostructures have demonstrated their incredible power in driving emergent electronic phenomena, some of which are reminiscent of those usually only observed in bulk strongly correlated quantum materials. With the recent discovery of van der Waals 𝑓-electron materials, the design of novel MSLs of intrinsic strong correlation is now within the reach. Here we study the novel electron phases of two-dimensional heavy-fermion MSL with increasingly diluted 𝑓-electron local moments. By applying dynamical mean-field theory with numerical renormalization group as an impurity solver, we demonstrate the appearance of a different energy scale and a reentrant Kondo breakdown in connection with the emergence of a flat band in the system. We further compare our numerical findings with predictions derived from the Lieb-Mattis theorem and show the necessity of this energy scale to consistently reconcile the predictions with the conventional single-impurity limit for exceedingly large unit cells.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Real-time evolution of Anderson impurity models via tensor network influence functionals

In this work, we present and analyze two tensor network-based influence functional approaches for simulating the real-time dynamics of quantum impurity models such as the Anderson model. Via comparison with recent numerically exact simulations, we show that such methods accurately capture the long-time nonequilibrium quench dynamics. The two parameters that must be controlled in these tensor network influence functional approaches are a time discretization (Trotter) error and a bond dimension (tensor network truncation) error. We show that the actual numerical uncertainties are controlled by an intricate interplay of these two approximations, which we demonstrate in different regimes. Our work opens the door to using these tensor network influence functional methods as general impurity solvers.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Advances in Quantum Defect Embedding Theory

Quantum defect embedding theory (QDET) is a many-body embedding method designed to describe condensed systems with strongly correlated electrons localized within a given region of space, for example spin defects in semiconductors and insulators. Although the QDET approach has been successful in predicting the electronic properties of several point defects, several limitations of the method remain. Here, in this work, we propose multiple advances to the QDET formalism. We derive a doublecounting correction that consistently treats the frequency dependence of the screened Coulomb interaction, and we illustrate the effect of including unoccupied orbitals in the active space. In addition, we propose a method to describe hybridization effects between the active space and the environment, and we compare the results of several impurity solvers, providing further insights into improving the reliability and applicability of the method. We present results for defects in diamond and for molecular qubits, including a detailed comparison with experiments.

Chen, Siyuan [University of Chicago, IL (United St↗
DOE OSTI2023

Local Excitations of a Charged Nitrogen Vacancy in Diamond with Multireference Density Matrix Embedding Theory

Here, we investigate the negatively charged nitrogen-vacancy center in diamond using periodic density matrix embedding theory (pDMET). To describe the strongly correlated excited states of this system, the complete active space self-consistent field (CASSCF) followed by n-electron valence state second-order perturbation theory (NEVPT2) was used as the impurity solver. Since the NEVPT2-DMET energies show a linear dependence on the inverse of the size of the embedding subspace, we performed an extrapolation of the excitation energies to the nonembedding limit using a linear regression. The extrapolated NEVPT2-DMET first triplet–triplet excitation energy is 2.31 eV and that for the optically inactive singlet–singlet transition is 1.02 eV, both in agreement with the experimentally observed vertical excitation energies of ∼2.18 eV and ∼1.26 eV, respectively. This is the first application of pDMET to a charged periodic system and the first investigation of the NV – defect using NEVPT2 for periodic supercell models.

36 MATERIALS SCIENCE↗