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arXiv:2512.23237 · Physical Review Research

Multiorbital dynamical mean-field theory with a complex-time solver

Yang Yu, Lei Zhang, Emanuel Gull, Xiaodong Cao, Xinyang Dong

Published Apr 2, 2026• 0 citations
arXivHTMLPDF

Abstract

We present the combination of a complex-time tensor-network impurity solver with an analytic continuation scheme based on exponential fitting as an efficient framework for single and multiorbital dynamical mean-field calculations. By performing time evolution along a complex-time contour, the approach balances computational cost with the difficulty of spectral recovery, offering greater flexibility than methods confined to the real or imaginary axis. By complementing the complex-time evolution with an exponential fitting scheme, we faithfully extract real-time information at negligible cost. The resulting method obtains high-resolution spectra at a significantly lower computational cost than real-time evolution, offering a promising tool for studies of strongly correlated materials.

DOI
10.1103/yqv4-4vjx

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We present the combination of a complex-time tensor-network impurity solver with an analytic continuation scheme based on exponential fitting as an efficient framework for single and multiorbital dynamical mean-field calculations. By performing time evolution along a complex-time contour, the approach balances computational cost with the difficulty of spectral recovery, offering greater flexibility than methods confined to the real or imaginary axis. By complementing the complex-time evolution with an exponential fitting scheme, we faithfully extract real-time information at negligible cost. The resulting method obtains high-resolution spectra at a significantly lower computational cost than real-time evolution, offering a promising tool for studies of strongly correlated materials.
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We introduce a neural network impurity solver for real-frequency DMFT that employs a multihead cross-attention mechanism to map hybridization functions to spectral functions, conditioned on impurity parameters. Trained on high-quality MPS data from complex contour time evolution and incorporating derivative constraints with respect to the complex-time angle, our model achieves smooth generalization to the real-frequency axis. Benchmarking on the single-band Hubbard model for the Bethe lattice demonstrates quantitative accuracy across metallic, strongly correlated, and insulating regimes.
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We propose a mixed-configuration approximation based on single-band impurity solvers to efficiently study nonequilibrium multiorbital systems at moderate computational cost. In this work, we merge the approach with the so-called auxiliary master equation approach. As a benchmark, we first show that our approach reproduces the results of quantum Monte Carlo (QMC) for two-orbital impurity models at equilibrium with overall good accuracy, especially for nondegenerate orbitals. We then use our approach as an impurity solver for dynamical mean-field theory (DMFT) to address the case of a two-orbital, realistic layered structure, recovering the strong crystal-field-driven charge polarization observed by solving the DMFT self-consistent cycle with QMC, albeit slightly reduced. Finally, we address a prototype nonequilibrium setup by sandwiching this layer between metallic contacts subject to a bias voltage described by different chemical potentials. This simplified model demonstrates our method's potential to access nonequilibrium steady-state behavior of multiorbital, realistic materials. These findings provide a first-step basis for theoretical studies of nonequilibrium properties of multiorbital compounds directly in the real frequency domain.
As quantum systems evolve in time, their entanglement usually grows quickly, making tensor network methods inefficient. ``Imaginary time'' evolution is efficient, but extrapolating back to the real axis is ill-conditioned. Here, the authors show that complex time, a mixture of the two, remains efficient while allowing a controlled reconstruction technique. Therefore, one can reach significantly longer times, which they demonstrate by obtaining high-accuracy results for impurity models at low energies.