Lehmann representation of the nonequilibrium self-energy

Abstract

It is shown that the non-equilibrium self-energy of an interacting lattice-fermion model has a unique Lehmann representation. Based on the construction of a suitable non-interacting effective medium, we provide an explicit and numerically practicable scheme to construct the Lehmann representation for the self-energy, given the Lehmann representation of the single-particle non-equilibrium Green's function. This is of particular importance for an efficient numerical solution of Dyson's equation in the context of approximations where the self-energy is obtained from a reference system with a small Hilbert space. As compared to conventional techniques to solve Dyson's equation on the Keldysh contour, the effective-medium approach allows to reach a maximum propagation time which can be several orders of magnitude longer. This is demonstrated explicitly by choosing the non-equilibrium cluster-perturbation theory as a simple approach to study the long-time dynamics of an inhomogeneous initial state after a quantum quench in the Hubbard model on a 10 x 10 square lattice. We demonstrate that the violation of conservation laws is moderate for weak Hubbard interaction and that the cluster approach is able to describe prethermalization physics.

12 pages, 7 figures, v2 with minor changes

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• Many-Body Physics with Ultracold Gases
• Thermalization and its mechanism for generic isolated quantum systems
• The Magnus expansion and some of its applications
• Quench dynamics and non equilibrium phase diagram of the Bose-Hubbard model
• Interaction Quench in the Hubbard model
• Dynamical phase transition in correlated fermionic lattice systems
• Iterative real-time path integral approach to nonequilibrium quantum transport
• Variational cluster approach to the Hubbard model: Phase-separation tendency and finite-size effects
• Diagrammatic expansion for positive spectral functions beyond GW: Application to vertex corrections in the electron gas
• Non-equilibrium cluster-perturbation theory

Cited by in corpus (11)

• Analytical Continuation of Matrix-Valued Functions: Carathéodory Formalism
• Stopping dynamics of ions passing through correlated honeycomb clusters
• Suppression and Control of Pre-thermalization in Multi-component Fermi Gases Following a Quantum Quench
• Topology of SmB${}_6$ determined by dynamical mean field theory
• Equivariant neural network for Green's functions of molecules and materials
• Total Energy Dynamics and Asymptotics of the Momentum Distribution Following an Interaction Quench in a Two-component Fermi Gas
• Interacting Chern Insulator in Infinite Spatial Dimensions
• Time-dependent Mott transition in the periodic Anderson model with nonlocal hybridization
• Diagrammatic Expansion for Positive Spectral Functions in the Steady-State Limit
• Non-equilibrium variational cluster perturbation theory: quench dynamics of the quantum Ising model
• Enforcing conservation laws in nonequilibrium cluster perturbation theory