Nonequilibrium dynamical mean-field theory and its applications

By H. Aoki, N. Tsuji, Martin Eckstein, M. Kollar, T. Oka, Philipp Werner. 2013

521 citations recorded by the source corpus.

The study of nonequilibrium phenomena in correlated lattice systems has developed into one of the most active and exciting branches of condensed matter physics. This research field provides rich new insights that could not be obtained from the study of equilibrium situations, and the theoretical understanding of the physics often requires the development of new concepts and methods. On the experimental side, ultrafast pump-probe spectroscopies enable studies of excitation and relaxation phenomena in correlated electron systems, while ultracold atoms in optical lattices provide a new way to control and measure the time evolution of interacting lattice systems with a vastly different characteristic time scale compared to electron systems. A theoretical description of these phenomena is challenging because, first, the quantum-mechanical time evolution of many-body systems out of equilibrium must be computed and second, strong-correlation effects which can be of a nonperturbative nature must be addressed. This review discusses the nonequilibrium extension of the dynamical mean field theory (DMFT), which treats quantum fluctuations in the time domain and works directly in the thermodynamic limit. The method reduces the complexity of the calculation via a mapping to a self-consistent impurity problem, which becomes exact in infinite dimensions. Particular emphasis is placed on a detailed derivation of the formalism, and on a discussion of numerical techniques, which enable solutions of the effective nonequilibrium DMFT impurity problem. Insights gained into the properties of the infinite-dimensional Hubbard model under strong nonequilibrium conditions are summarized. These examples illustrate the current ability of the theoretical framework to reproduce and understand fundamental nonequilibrium phenomena, such as the dielectric breakdown of Mott insulators, photodoping, and collapse-and-revival oscillations in quenched systems. Furthermore, remarkable novel phenomena have been predicted by the nonequilibrium DMFT simulations of correlated lattice systems, including dynamical phase transitions and field-induced repulsion-to-attraction conversions.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics

View Paper: https://www.semanticscholar.org/paper/de586252d9956dc20a7a3a9da8b37235ed908f2c

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In Atomic and Molecular Physics, and Optics

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Citations in the corpus

Diagrammatic routes to nonlocal correlations beyond dynamical mean field theory (2017, methodology): “Building on its success, DMFT nowadays is routinely employed for realistic material and non-equilibrium calculations, for reviews see Held et al., 2006, Kotliar et al., 2006, Held, 2007, Katsnelson et al., 2008 and Aoki et al., 2014, respectively.”
Colloquium: Nonthermal pathways to ultrafast control in quantum materials (2021, background): “…dynamical mean-field theory (DMFT) for strongly correlated systems, including Mott insulators with mainly local self-energies (Freericks, Turkowski, and Zlatić, 2006; Tsuji, Oka, and Aoki, 2008; Aoki et al., 2014), and the real-time functional renormalization group approach (Kennes et al., 2012).”
Quantum simulation with interacting photons (2016, methodology): “Keldysh path integral methods have been used to explore long-range properties [235, 240] and dynamical mean-field theory has been generalised to nonequilibrium scenarios [7].”
QuSpin: a Python Package for Dynamics and Exact Diagonalisation of Quantum Many Body Systems part I: spin chains (2016, methodology): “In contrast to the tremendous progress made in studying low-energy phenomena based on well-developed sophisticated techniques, such as Quantum Monte Carlo methods [1, 2, 3], Density Matrix Renormalisation Group [4, 5], Matrix Product States [6], Dynamical Mean-Field Theory [7, 8, 9], etc., one of th”
Efficient Variational Quantum Simulator Incorporating Active Error Minimization (2016, methodology): “This has motivated dynamical versions of many well-known techniques, e.g. nonequilibrium dynamical mean-ﬁeld theory [27], the time-dependent variational quantum Monte Carlo method [28], time-dependent tensor network methods [29, 30], and of course time-dependent density functional theory [31].”