Long-term memory magnetic correlations in the Hubbard model: A dynamical mean-field theory analysis

TL;DR

This paper studies long-term magnetic memory effects in the Hubbard model using dynamical mean-field theory, revealing their connection to the Mott transition and local moment physics, with implications for analyzing strongly correlated systems.

Contribution

It introduces a reliable method to evaluate long-term magnetic correlations from imaginary time data and applies it to the Hubbard model's Mott transition, highlighting new insights into many-electron spectrum properties.

Findings

Long-term magnetic memory exists in the Mott regime at low temperatures.

Memory effects abruptly end at the first-order Mott transition.

Gradual onset of infinite decay near the Widom line at higher temperatures.

Abstract

We investigate the onset of a not-decaying asymptotic behavior of temporal magnetic correlations in the Hubbard model in infinite dimensions. This long-term memory feature of dynamical spin correlations can be precisely quantified by computing the difference between the zero-frequency limit of the Kubo susceptibility and the corresponding static isothermal one. Here, we present a procedure for reliably evaluating this difference starting from imaginary time-axis data, and apply it to the testbed case of the Mott-Hubbard metal-insulator transition (MIT). At low temperatures, we find long-term memory effects in the entire Mott regime, abruptly ending at the first order MIT. This directly reflects the underlying local moment physics and the associated degeneracy in the many-electron spectrum. At higher temperatures, a more gradual onset of an infinitely-long time-decay of magnetic correlations occurs in the crossover regime, not too far from the Widom line emerging from the critical point of the MIT. Our work has relevant algorithmic implications for the analytical continuation of dynamical susceptibilities in strongly correlated regimes and offers a new perspective for unveiling fundamental properties of the many-particle spectrum of the problem under scrutiny.