Real-Time DMFT Scheme Achieves Stable Convergence for Near-Term Quantum Simulation

Scientists are tackling a major hurdle in materials science , accurately simulating the complex behaviour of strongly correlated quantum systems. Chakradhar Rangi, Aadi Singh, and Ka-Ming Tam, all from Louisiana State University, have developed a novel real-time iteration scheme for Dynamical Mean-Field Theory (DMFT) that promises to unlock new possibilities for near-term quantum simulation. Their research, detailed in a new paper, moves beyond traditional imaginary-time DMFT approaches by operating directly with real-time quantities, making it ideally suited for implementation on emerging quantum hardware with limited resources. By mapping the problem onto a simplified one-dimensional chain and iteratively updating the hybridization function, the team demonstrates stable convergence and accurately captures the metal-to-insulator transition in the Hubbard model , delivering detailed spectral features with improved efficiency and compatibility for quantum platforms.

Unlike conventional DMFT methods that rely on imaginary time or frequency spaces, this new approach operates directly with real-time dynamics, making it ideally suited for implementation on emerging quantum computing hardware with limited resources. The research team mapped the challenging impurity problem onto a simplified one-dimensional chain consisting of a small number of bath sites, which was then solved using exact diagonalization as a crucial proof-of-concept step. This innovative technique iteratively updates the hybridization function through time-domain fitting, achieving self-consistency without the need for numerically unstable conversions between time and frequency domains.

The study successfully demonstrated stable convergence across a broad spectrum of interaction strengths for the half-filled Hubbard model on a Bethe lattice, accurately capturing the critical metal-to-insulator transition. Despite employing limited time resolution and a minimal discretization of the bath, the resulting spectral functions clearly revealed the emergence of distinct Hubbard bands and a noticeable suppression of spectral weight at the Fermi level as interaction strength increased. This achievement overcomes significant limitations inherent in simpler two-site DMFT approximations, delivering detailed spectral features while maintaining computational efficiency and compatibility with quantum platforms through real-time dynamics. The work establishes a robust framework for simulating strongly correlated materials using near-term quantum devices.
This breakthrough addresses a major hurdle in simulating complex quantum many-body systems, where classical methods often struggle with the exponential growth of computational demands. By formulating the DMFT equations directly in the time domain, the researchers circumvent the need for computationally expensive frequency-space transformations, streamlining the process for quantum implementation. The team’s approach enables the simulation of larger effective baths with minimal qubit and gate requirements, aligning with the constraints of current and near-future quantum hardware. The iterative time-domain fitting of the hybridization function provides a stable and efficient pathway to self-consistency, paving the way for more accurate and scalable DMFT calculations.

Experiments show that the method accurately reproduces key features of the Hubbard model, including the formation of Hubbard bands, signatures of strong electron correlation, and the suppression of spectral weight at the Fermi level, which indicates the transition from a metallic to an insulating state. This level of detail is often inaccessible to simplified DMFT approximations, highlighting the power of the new time-domain approach. The. The team mapped the effective impurity problem onto a finite one-dimensional chain comprising a small number of bath sites, solved via exact diagonalization as a proof-of-concept, demonstrating a robust and efficient methodology.

Experiments revealed stable convergence across a wide range of interaction strengths for the half-filled Hubbard model on a Bethe lattice, successfully capturing the crucial metal-to-insulator transition. Results demonstrate that the new scheme accurately simulates the behaviour of correlated electron systems, even with limited computational resources. The researchers achieved stable convergence even with limited time resolution and minimal bath discretization, a significant technical accomplishment. Measurements confirm the emergence of Hubbard bands, spectral features indicative of strong electron correlations, and the suppression of spectral weight at the Fermi level as interaction strength increases.

This is a critical finding, as these features were previously inaccessible using simpler two-site DMFT approximations, highlighting the enhanced accuracy of this new approach. Tests prove that the algorithm can effectively handle strong electron correlations, a notoriously difficult problem in condensed matter physics. The team measured the spectral functions, observing clear evidence of the metal-to-insulator transition as the interaction strength was varied. Data shows that the method maintains minimal qubit and gate depth requirements, making it particularly suitable for implementation on near-term quantum devices with limited Hilbert spaces.

The breakthrough delivers a framework for capturing key spectral features via DMFT simulations on these platforms, opening up new avenues for exploring complex materials. Furthermore, the study establishes a robust framework for simulating larger effective baths while respecting the constraints of near-term devices. Scientists recorded detailed spectral features, confirming the accuracy and efficiency of the real-time dynamics approach. Measurements confirm that the algorithm’s performance is stable across a broad spectrum of interaction strengths, demonstrating its versatility and reliability. This approach differs from conventional DMFT methods which typically operate in imaginary time or frequency space, offering advantages for near-term hardware with limited computational resources. The researchers mapped the effective impurity problem onto a finite one-dimensional chain, solved using exact diagonalization as a proof of concept, and iteratively updated the hybridization function until self-consistency was achieved. The findings demonstrate stable convergence across a range of interaction strengths for the half-filled Hubbard model on a Bethe lattice, successfully capturing the metal-to-insulator transition.

Despite employing limited time resolution and a minimal bath discretization, the resulting spectral functions clearly exhibited the emergence of Hubbard bands and suppression of spectral weight at the Fermi level as interaction strength increased, a key feature of the Mott insulating state. The authors acknowledge limitations related to the chosen resolution and bath size, but highlight the method’s ability to deliver detailed spectral features beyond the capabilities of simpler two-site DMFT approximations. Future research will focus on replacing the exact diagonalization solver with a quantum computing-based solver, potentially enabling calculations beyond perturbative methods or the two-site approximation. Exploring non-equilibrium DMFT, extending the method to treat non-local interactions via Extended DMFT, and combining it with Real-Space DMFT to study inhomogeneous systems are also promising avenues for investigation.