Speaker
Description
Recent progress in time-resolved Raman scattering and resonant inelastic X-ray scattering has made it possible to follow how low-energy charge, spin, and phonon excitations evolve in time. These measurements have also been shown to provide higher-order quantities beyond the spectra, like the quantum Fisher information, which is drawing attention as a new way to characterize nonequilibrium states [1].
From a theoretical point of view, both the spectra and such quantities are described by nonequilibrium two-particle correlation functions. Although their dynamics could in principle be computed from the nonequilibrium Bethe–Salpeter equation, the required computational time and memory are prohibitive. In practice, conventional approaches therefore neglect vertex corrections, thereby omitting collective effects.
To address this problem, we present a framework in which vertex corrections are included naturally. It builds on the generalized Keldysh formalism [2], applied to a Hamiltonian supplemented by a virtual external probe field [3]. We derive a linear integral equation for the correlation functions and develop an efficient solver for it based on quantics tensor trains [4], a tensor network technique [5].
In this presentation, we introduce the formalism and demonstrate it by studying the fluctuation dynamics of nonequilibrium antiferromagnetic states in the Hubbard model. We find that including vertex corrections alters the dynamics qualitatively, and that fluctuations grow in the vicinity of a nonthermal critical point [6].
[1] D. R. Baykusheva et al., Phys. Rev. Lett. 130, 106902 (2023).
[2] E. Canovi, P. Werner, and M. Eckstein, Phys. Rev. Lett. 113, 265702 (2014).
[3] O. P. Matveev, A. M. Shvaika, and J. K. Freericks, Phys. Rev. B 113, 195148 (2026).
[4] H. Shinaoka et al., Phys. Rev. X 13, 021015 (2023).
[5] K. Inayoshi, H. Shinaoka, and Y. Murakami, arXiv:2607.11055.
[6] N. Tsuji, M. Eckstein, and P. Werner. Phys. Rev. Lett. 110, 136404 (2013).