Non-equilibrium evolution of the optical conductivity of the weakly interacting Hubbard model: Drude response and $\pi$-ton type vertex corrections

Abstract

The optical conductivity contains information about energy absorption and the underlying physical processes. In finite-dimensional systems, vertex corrections to the bare bubble need to be considered, which is a computationally challenging task. Recent numerical studies showed that in the weak coupling limit, near an ordering instability with wave vector $\pi$, $\pi$-tons (or Maki-Thompson diagrams) yield the most relevant vertex corrections. This provides a route for including vertex corrections into, for example, dynamical mean field theory estimates of the optical conductivity. By implementing calculations on the Kadanoff-Baym contour, we reveal the characteristic spectral signatures of the $\pi$-tons and their evolution under non-equilibrium conditions. We consider interaction quenches of the weakly-correlated Hubbard model near the antiferromagnetic phase boundary, and analyze the evolution of the Drude and $\pi$-ton features. While the bubble contribution to the optical conductivity is found to thermalize rapidly, after some oscillations with frequencies related to the local spectral function, the $\pi$-ton contribution exhibits a slower evolution. We link this observation to the prethermalization phenomenon which has been previously studied in weakly interacting, quenched Hubbard models.

arXiv comment15 pages, 12 figures

References in corpus (25)

• Quantum Cluster Theories
• Experimental realization of a long-range antiferromagnet in the Hubbard model with ultracold atoms
• Nonequilibrium dynamical mean-field theory and its applications
• Quench dynamics and non equilibrium phase diagram of the Bose-Hubbard model
• Prethermalization
• Interaction Quench in the Hubbard model
• Dynamical phase transition in correlated fermionic lattice systems
• Diagrammatic routes to nonlocal correlations beyond dynamical mean field theory
• Non-perturbative many-body approach to the Hubbard model and single-particle pseudogap
• Strongly correlated fermions after a quantum quench
• Nonequilibrium dynamical mean-field theory
• A New Iterative Perturbation Scheme for Lattice Models with Arbitrary Filling
• Interaction-induced adiabatic cooling and antiferromagnetism of cold fermions in optical lattices
• Imaging and addressing of individual fermionic atoms in an optical lattice
• Interaction quench in the Hubbard model: Relaxation of the spectral function and the optical conductivity
• Nonthermal antiferromagnetic order and nonequilibrium criticality in the Hubbard model
• NESSi: The Non-Equilibrium Systems Simulation package
• Influence of Spatial Correlations in Strongly Correlated Electron Systems: Extension to Dynamical Mean Field Approximation
• Optical and DC conductivity of the two-dimensional Hubbard model in the pseudogap regime and across the antiferromagnetic quantum critical point, including vertex corrections
• Nonequilibrium dynamical mean-field theory based on weak-coupling perturbation expansions: Application to dynamical symmetry breaking in the Hubbard model
• Generic optical excitations of correlated systems: $\pi$-tons
• Benchmark of a modified Iterated Perturbation Theory approach on the 3d FCC lattice at strong coupling
• Electronic and fluctuation dynamics following a quench to the superconducting phase
• Dynamical instabilities and transient short-range order in the fermionic Hubbard model
• Diagrammatic study of optical excitations in correlated systems

Cited by in corpus (6)

• Nonequilibrium Two-Particle Self-Consistent Approach
• Dynamical Mean Field Theory extension to the nonequilibrium Two-Particle Self-Consistent approach
• LinReTraCe: The Linear Response Transport Centre
• Displaced Drude peak from $\pi$-ton vertex corrections
• Nonequilibrium DMFT approach to time-resolved Raman spectroscopy
• Analytical expression for $\pi$-ton vertex contributions to the optical conductivity