Naoto Tsuji

Nonequilibrium dynamical mean-field theory and its applications

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.

Light-induced collective pseudospin precession resonating with Higgs mode in a superconductor

Optically manipulating superconductors In superconductors, electrons of opposite momenta pair to form a highly correlated state that manages to flow without encountering any resistance. Matsunaga et al. manipulated the wavefunction of these pairs in the superconductor NbN with an electromagnetic pulse that they transmitted through a thin layer of the material (see the Perspective by Pashkin and Leitenstorfer). The superconducting gap, which is the energy needed to break the pairs apart, oscillated at twice the frequency of the pulses electric field. When they matched this frequency to half the gap, the authors excited a collective mode in the superconductor called the Higgs mode, a relative of the Higgs boson in particle physics. Science, this issue p. 1145; see also p. 1121 Terahertz pump-probe spectroscopy reveals the oscillations of a superconducting order parameter at twice the pump frequency. [Also see Perspective by Pashkin and Leitenstorfer] Superconductors host collective modes that can be manipulated with light. We show that a strong terahertz light field can induce oscillations of the superconducting order parameter in NbN with twice the frequency of the terahertz field. The result can be captured as a collective precession of Anderson’s pseudospins in ac driving fields. A resonance between the field and the Higgs amplitude mode of the superconductor then results in large terahertz third-harmonic generation. The method we present here paves a way toward nonlinear quantum optics in superconductors with driving the pseudospins collectively and can be potentially extended to exotic superconductors for shedding light on the character of order parameters and their coupling to other degrees of freedom.

Dynamical band flipping in fermionic lattice systems: an ac-field-driven change of the interaction from repulsive to attractive.

We show theoretically that the sudden application of an appropriate ac field to correlated lattice fermions flips the band structure and effectively switches the interaction from repulsive to attractive. The nonadiabatically driven system is characterized by a negative temperature with a population inversion. We numerically demonstrate the converted interaction in an ac-driven Hubbard model with the nonequilibrium dynamical mean-field theory solved by the continuous-time quantum Monte Carlo method. Based on this, we propose an efficient ramp-up protocol for ac fields that can suppress heating, which leads to an effectively attractive Hubbard model with a temperature below the superconducting transition temperature of the equilibrium system.

Correlated electron systems periodically driven out of equilibrium: Floquet + DMFT formalism

We propose to combine the Floquet formalism for systems in ac fields with the dynamical mean-field theory to study correlated electron systems periodically driven out of equilibrium by external fields such as intense laser light. This approach has a virtue that we can nonperturbatively include both the correlation effects and nonlinear effects due to the driving field, which is imperative in analyzing recent experiments for photoinduced phase transitions. In solving the problem, we exploit a general theorem that the Hamiltonian in a Floquet matrix form can be exactly diagonalized for single-band noninteracting systems. As a demonstration, we have applied the method to the Falicov-Kimball model in intense ac fields to calculate the spectral function. The result shows that photoinduced midgap states emerge from strong ac fields, triggering an insulator-metal transition.

Brillouin-Wigner theory for high-frequency expansion in periodically driven systems: Application to Floquet topological insulators

We construct a systematic high-frequency expansion for periodically driven quantum systems based on the Brillouin-Wigner (BW) perturbation theory, which generates an effective Hamiltonian on the projected zero-photon subspace in the Floquet theory, reproducing the quasienergies and eigenstates of the original Floquet Hamiltonian up to desired order in

Nonthermal antiferromagnetic order and nonequilibrium criticality in the Hubbard model.

1/\omega

Ordered phases in the Holstein-Hubbard model: Interplay of strong Coulomb interaction and electron-phonon coupling

, with

Nonequilibrium Steady State of Photoexcited Correlated Electrons in the Presence of Dissipation

\omega

Nonthermal symmetry-broken states in the strongly interacting Hubbard model

being the frequency of the drive. The advantage of the BW method is that it is not only efficient in deriving higher-order terms, but even enables us to write down the whole infinite series expansion, as compared to the van Vleck degenerate perturbation theory. The expansion is also free from a spurious dependence on the driving phase, which has been an obstacle in the Floquet-Magnus expansion. We apply the BW expansion to various models of noninteracting electrons driven by circularly polarized light. As the amplitude of the light is increased, the system undergoes a series of Floquet topological-to-topological phase transitions, whose phase boundary in the high-frequency regime is well explained by the BW expansion. As the frequency is lowered, the high-frequency expansion breaks down at some point due to band touching with nonzero-photon sectors, where we find numerically even more intricate and richer Floquet topological phases spring out. We have then analyzed, with the Floquet dynamical mean-field theory, the effects of electron-electron interaction and energy dissipation. We have specifically revealed that phase transitions from Floquet-topological to Mott insulators emerge, where the phase boundaries can again be captured with the high-frequency expansion.

Theory of Anderson pseudospin resonance with Higgs mode in superconductors

We study dynamical phase transitions from antiferromagnetic to paramagnetic states driven by an interaction quench in the fermionic Hubbard model using the nonequilibrium dynamical mean-field theory. We identify two dynamical transition points where the relaxation behavior qualitatively changes: one corresponds to the thermal phase transition at which the order parameter decays critically slowly in a power law ∝t(-1/2), and the other is connected to the existence of nonthermal antiferromagnetic order in systems with effective temperature above the thermal critical temperature. The frequency of the amplitude mode extrapolates to zero as one approaches the nonthermal (quasi)critical point, and thermalization is significantly delayed by the trapping in the nonthermal state. A slow relaxation of the nonthermal order is followed by a faster thermalization process.