Out-of-time-ordered correlators of the Hubbard model: SYK strange metal in the spin freezing crossover region

Abstract

The Sachdev-Ye-Kitaev (SYK) model describes a strange metal that shows peculiar non-Fermi liquid properties without quasiparticles. It exhibits a maximally chaotic behavior characterized by out-of-time-ordered correlators (OTOCs), and is expected to be a holographic dual to black holes. Recently, a striking similarity between the SYK model and the Hund-coupling induced spin-freezing crossover in multi-orbital Hubbard models has been pointed out. To further explore this connection, we study OTOCs for fermionic Hubbard models, which are prototypical models for strongly correlated electrons in solids. We introduce an imaginary-time four-point correlation function with an appropriate time ordering, which by means of the spectral representation and the out-of-time-order fluctuation-dissipation theorem can be analytically continued to real-time OTOCs. Based on this approach, we numerically evaluate real-time OTOCs for Hubbard models in the thermodynamic limit, using the dynamical mean-field theory in combination with a numerically exact continuous-time Monte Carlo impurity solver. The results for the single-orbital model show that a certain spin-related OTOC captures local moment formation in the vicinity of the metal-insulator transition, while the self-energy does not show SYK-like non-Fermi liquid behavior. On the other hand, for the two- and three-orbital models with nonzero Hund coupling we find that the OTOC exhibits a rapid damping at short times and an approximate power-law decay at longer times in the spin-freezing crossover regime characterized by fluctuating local moments and a non-Fermi liquid self-energy $\Sigma (\omega )\sim \sqrt{\omega }$. These results are in a good agreement with the behavior of the SYK model, providing firm evidence for the close relation between the spin-freezing crossover physics of multi-orbital Hubbard models and the SYK strange metal.

37 pages, 14 figures

References in corpus (14)

• Continuous-time Monte Carlo methods for quantum impurity models
• Strong electronic correlations from Hund's coupling
• The ALPS project release 1.3: open source software for strongly correlated systems
• Hybridization expansion impurity solver: General formulation and application to Kondo lattice and two-orbital models
• Lyapunov Exponent and Out-of-Time-Ordered Correlator's Growth Rate in a Chaotic System
• Diagrammatic Monte Carlo simulation of non-equilibrium systems
• Spin freezing transition and non-Fermi-liquid self-energy in a 3-orbital model
• Microscopic model of quantum butterfly effect: out-of-time-order correlators and traveling combustion waves
• Quantum chaos on a critical Fermi surface
• Characterizing Many-Body Localization by Out-of-Time-Ordered Correlation
• Exact out-of-time-ordered correlation functions for an interacting lattice fermion model
• Nonlinear sigma model approach to many-body quantum chaos: Regularized and unregularized out-of-time-ordered correlators
• A spin-freezing perspective on cuprates
• Spin freezing and the Sachdev-Ye model

Cited by in corpus (8)

• Sachdev-Ye-Kitaev Models and Beyond: A Window into Non-Fermi Liquids
• $T$-linear resistivity in models with local self-energy
• Quantum bounds and fluctuation-dissipation relations
• T-linear resistivity, optical conductivity and Planckian transport for a holographic local quantum critical metal in a periodic potential
• Deconfined critical point in a doped random quantum Heisenberg magnet
• Dynamical transition from localized to uniform scrambling in locally hyperbolic systems
• Strange Metal Solution in the Diagrammatic Theory for the $2d$ Hubbard Model
• Out of Time Order Correlation of the Hubbard Model with Random Local Disorder