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Results for “Anderson impurity model”

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12 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Dynamic, symmetry-preserving, and hardware-adaptable circuits for quantum computing many-body states and correlators of the Anderson impurity model

We present a hardware-reconfigurable ansatz on N q -qubits for the variational preparation of many-body states of the Anderson impurity model (AIM) with N imp + N bath = N q /2 sites, which conserves total charge and spin z component within each variational search subspace. The many-body ground state of the AIM is determined as the minimum over all minima of O(N$^2_ q$) distinct charge-spin sectors. Hamiltonian expectation values are shown to require ω(N q ) < N meas. $\leqslant$ O(N imp N bath ) symmetry-preserving, parallelizable measurement circuits, each amenable to postselection. To obtain the one-particle impurity Green’s function we show how initial Krylov vectors can be computed via midcircuit measurement and how Lanczos iterations can be computed using the symmetry-preserving ansatz. For a single-impurity Anderson model with a number of bath sites increasing from one to seven, we show using numerical emulation that the ease of variational ground-state preparation is suggestive of linear scaling in circuit depth and subquartic scaling in optimizer complexity. We therefore expect that, combined with time-dependent methods for Green’s function computation, our ansatz provides a useful tool to account for electronic correlations on early fault-tolerant processors. Finally, with a view towards computing real materials properties of interest like magnetic susceptibilities and electron-hole propagators, we provide a straightforward method to compute many-body, time-dependent correlation functions using a combination of time evolution, midcircuit measurement-conditioned operations, and the Hadamard test.

36 MATERIALS SCIENCE↗
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 OSTI2026

Particle-hole symmetric slave-boson method for the mixed valence problem

We introduce an analytic slave-boson method for treating the finite-𝑈 Anderson impurity model. Our approach introduces two bosons to track both 𝑄 ⇌ 𝑄 ± 1 valence fluctuations and reduces to a single symmetric 𝑠 boson in the effective action, encoding all the high-energy atomic physics information in the boson's kinematics, while the low-energy part of the action remains unchanged across finite-𝑈, infinite-𝑈, and Kondo limits. We recover the infinite-𝑈- and Kondo-limit actions from our approach and show that the Kondo resonance already develops in the normal state when the slave boson has yet to condense. We show that the slave rotor and 𝑠 boson have the same algebraic structure, and we establish a unified functional integral framework connecting the 𝑠-boson and slave-rotor representations for the single-impurity Anderson model.

Anderson impurity model↗
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 OSTI2026

Kondo effect in ferromagnetic quantum critical CeRh 6 ⁢Ge 4

The mechanism of a pressure-induced quantum critical point in the heavy fermion ferromagnet CeRh 6 ⁢Ge 4 has attracted interest, as ferromagnetic quantum criticality in a clean itinerant Ce compound is typically avoided. The localized versus itinerant character of the 4⁢𝑓 electrons is a key aspect for understanding this behavior. We investigated the electronic structure of the 4⁢𝑓 shell in CeRh 6 ⁢Ge 4 using core-level photoelectron and x-ray absorption spectroscopy, demonstrating the hybridization of Ce 4⁢𝑓 with the conduction electrons. Linearly polarized x-ray absorption reveals a temperature-dependent linear dichroism consistent with the crystal-electric-field sequence as inferred from the static susceptibility. This dichroism cannot be described by an ionic full-multiplet model alone, but is reproduced by including the Kondo effect within a single-impurity Anderson model in the noncrossing approximation. The Kondo effect mixes higher-lying crystal-field states into a resulting multiorbital ground state with 4⁢𝑓 occupancy, 𝑛 𝑓 ∼ 0.9. Deviations at low temperatures between the measured linear dichroism and calculated dichroism suggest an orbital-dependent Kondo effect. A scenario in which there is a multiorbital ground state and orbital-dependent Kondo hybridization should be a starting point for a model of pressure-induced criticality in CeRh 6 ⁢Ge 4 .

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 OSTI2024

Exploring the exact limits of the real-time equation-of-motion coupled cluster cumulant Green’s functions

In this paper, we analyze the properties of the recently proposed real-time equation-of-motion coupled-cluster (RT-EOM-CC) cumulant Green’s function approach [Rehr et al., J. Chem. Phys. 152, 174113 (2020)]. We specifically focus on identifying the limitations of the original time-dependent coupled cluster (TDCC) ansatz and propose an enhanced double TDCC ansatz, ensuring the exactness in the expansion limit. In addition, we introduce a practical cluster-analysis-based approach for characterizing the peaks in the computed spectral function from the RT-EOM-CC cumulant Green’s function approach, which is particularly useful for the assignments of satellite peaks when many-body effects dominate the spectra. Our preliminary numerical tests focus on reproducing, approximating, and characterizing the exact impurity Green’s function of the three-site and four-site single impurity Anderson models using the RT-EOM-CC cumulant Green’s function approach. The numerical tests allow us to have a direct comparison between the RT-EOM-CC cumulant Green’s function approach and other Green’s function approaches in the numerical exact limit.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Distinct effect of Kondo physics on crystal field splitting in electron and spin spectroscopies

Magnetic anisotropy is a key feature of rare earth materials from permanent magnets to heavy fermions. Here we explore the complex interplay of Kondo physics and anisotropy, and their effect on different experimental probes of magnetic anisotropy in a minimal 𝐽=3/2 Anderson impurity model using the numerical renormalization group. While anisotropy suppresses Kondo screening, virtual valence fluctuations enhance the anisotropy. We find distinct renormalization of the magnetic anisotropy measured via dynamical spin response (inelastic neutron scattering) versus electronic excitations in the impurity spectral function (resonant inelastic x-ray and scanning tunneling spectroscopy). The two measurement types have different responses and dependencies on the temperature and Kondo scales.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Oscillate and renormalize: Fast phonons reshape the Kondo effect in flat-band systems

Here, we examine the interplay between electron correlations and phonons in an Anderson-Holstein impurity model with an Einstein phonon. When the phonons are slow compared to charge fluctuations (frequency 𝜔 0 ≪ 𝑈/2, the onsite Coulomb scale 𝑈/2), we demonstrate analytically that the expected phonon-mediated reduction of interactions is completely suppressed, even in the strong-coupling regime. This suppression arises from the oscillator's inability to respond to rapid charge fluctuations, manifested as a compensation effect between the polaronic cloud and the excited-state phonons associated with valence fluctuations. We identify a frozen mixed valence phase, above a threshold dimensionless electron-phonon coupling 𝛼* when the phonons are slow, where the static phonon cloud locks the impurity into specific valence configurations, potentially explaining the puzzling coexistence of mixed valence behavior and insulating properties in materials like rust. Conversely, when the phonon is fast (𝜔 0 ≳ 𝑈/2), the system exhibits conventional polaronic behavior with renormalized onsite interactions effectively 𝑈 eff due to phonon-mediated attraction, with additional satellite features in the local spectral function due to phonon excitations. Using numerical renormalization group calculations, a fully dynamic renormalization technique, we confirm these behaviors in both regimes. These findings have important implications for strongly correlated systems where phonon energy scales may be comparable to the Coulomb scale, such as in twisted bilayer graphene, necessitating careful consideration of interaction renormalizations in theoretical models.

Anderson impurity model↗
DOE OSTI2026

Coupled Lindblad Pseudomode Theory for Simulating Open Quantum Systems

Coupled Lindblad pseudomode theory is a promising approach for simulating non-Markovian quantum dynamics on both classical and quantum platforms, with dynamics that can be realized as a quantum channel. We provide theoretical evidence that the number of coupled pseudomodes only needs to scale as polylog⁡(𝑇/𝜖) in the simulation time 𝑇 and precision 𝜖. Inspired by the realization problem in control theory, we also develop a robust numerical algorithm for constructing the coupled modes that avoid the nonconvex optimization required by existing approaches. We demonstrate the effectiveness of our method by computing population dynamics and absorption spectra for the spin-boson model. Furthermore, this Letter provides a significant theoretical and computational improvement to the coupled Lindblad framework, which impacts a broad range of applications from classical simulations of quantum impurity problems to quantum simulations on near-term quantum platforms.

Anderson impurity model↗
DOE OSTI2024

Quasi-Lindblad pseudomode theory for open quantum systems

Here, we introduce a new framework to study the dynamics of open quantum systems with linearly coupled Gaussian baths. Our approach replaces the continuous bath with an auxiliary discrete set of pseudomodes with dissipative dynamics, but we further relax the complete positivity requirement in the Lindblad master equation and formulate a quasi-Lindblad pseudomode theory. We show that this quasi-Lindblad pseudomode formulation directly leads to a representation of the bath correlation function in terms of a complex weighted sum of complex exponentials, an expansion that is known to be rapidly convergent in practice and thus leads to a compact set of pseudomodes. The pseudomode representation is not unique and can differ by a gauge choice. When the global dynamics can be simulated exactly, the system dynamics is unique and independent of the specific pseudomode representation. However, the gauge choice may affect the stability of the global dynamics, and we provide an analysis of why and when the global dynamics can retain stability despite losing positivity. We showcase the performance of this formulation across various spectral densities in both bosonic and fermionic problems, finding significant improvements over conventional pseudomode formulations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Surface Local Impurity Scattering as a Probe for Topological Kondo Insulators

Shortly after the discovery of topological band insulators, topological Kondo insulators (TKIs) is also theoretically predicted. The latter has ignited revival interest in the properties of Kondo insulators. Currently, the feasibility of topological nature in SmB 6 is intensively analyzed by several complementary probes. Here by starting with a minimal-orbital Anderson lattice model, the local electronic structure is explored in a Kondo insulator. It is showed that the two strong topological regimes sandwiching the weak topological regime give rise to a single Dirac cone, which is located near the center or corner of the surface Brillouin zone. It is further found that, when a single impurity is placed on the surface, low-energy resonance states are induced in the weak scattering limit for the strong TKI regimes and the resonance level moves monotonically across the hybridization gap with the strength of impurity scattering potential; while low energy states can only be induced in the unitary scattering limit for the weak TKI regime, where the resonance level moves universally toward the center of the hybridization gap. These impurity-induced low-energy quasiparticles will lead to characteristic signatures in scanning tunneling microscopy/spectroscopy, which has recently found success in probing into exotic properties in heavy fermion systems.

36 MATERIALS SCIENCE↗