Nonequilibrium self-energy functional theory

Abstract

The self-energy functional theory (SFT) is generalized to describe the real-time dynamics of correlated lattice-fermion models far from thermal equilibrium. This is achieved by means of a reformulation of the original equilibrium theory in terms of double-time Green's functions on the Keldysh-Matsubara contour. We construct a functional which is stationary at the physical (nonequilibrium) self-energy and which yields the grand potential of the initial thermal state at the physical point. Non-perturbative approximations can be defined by specifying a reference system that serves to generate trial self-energies. These self-energies are varied by varying the reference system's one-particle parameters on the Keldysh-Matsubara contour. In case of thermal equilibrium, the new approach reduces to the conventional SFT. However, "unphysical" variations, i.e., variations that are different on the upper and the lower branch of the Keldysh contour, must be considered to fix the time-dependence of the optimal physical parameters via the variational principle. Functional derivatives in the nonequilibrium SFT Euler equation are carried out analytically to derive conditional equations for the variational parameters that are accessible to a numerical evaluation via a time-propagation scheme. Approximations constructed by means of the nonequilibrium SFT are shown to be inherently causal, internally consistent and to respect macroscopic conservation laws resulting from gauge symmetries of the Hamiltonian. This comprises the nonequilibrium dynamical mean-field theory but also dynamical-impurity and variational-cluster approximations that are specified by reference systems with a finite number of degrees of freedom. In this way, non-perturbative and consistent approximations can be set up, the numerical evaluation of which is accessible to an exact-diagonalization approach.

22 pages, 3 figures

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• A method to efficiently simulate the thermodynamical properties of the Fermi-Hubbard model on a quantum computer
• Variational cluster approach to thermodynamic properties of interacting fermions at finite temperatures: A case study of the two-dimensional single-band Hubbard model at half filling
• Auxiliary Hamiltonian representation of the nonequilibrium Dyson equation
• Build-up of the Kondo effect from real-time 2PI effective action for the Anderson impurity model
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• Lehmann representation of the nonequilibrium self-energy
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• Master equation based steady-state cluster perturbation theory
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• Time-dependent Mott transition in the periodic Anderson model with nonlocal hybridization
• Self-energy functional theory with symmetry breaking for disordered lattice bosons
• Non-equilibrium variational cluster perturbation theory: quench dynamics of the quantum Ising model
• Enforcing conservation laws in nonequilibrium cluster perturbation theory