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.

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Nonequilibrium dynamical mean-field theory and its applications

The present situation in theoretical and experimental studies on one-dimensional magnetic systems is fully discussed. Equal-time as well as the dynamic properties are included with an emphasis on the latter. Four model systems are examined in detail: TMMC (Heisenberg antiferromagnet), CsNiF3 (planar ferromagnet), CoCl2. 2NC5H5 (Ising ferromagnet), CuCl2. 2NC5H5 (Heisenberg antiferromagnet with S = ½). The equal-time properties are quite well understood in theory and in experiment but the dynamical properties much less so. The open questions and possible investigations for the future are discussed.

Theoretical and experimental studies on one-dimensional magnetic systems

Mechanisms of Mott transitions and d x 2 - y 2 -wave superconductivity (SC) are studied in the half-filled-band Hubbard model on square lattices with a diagonal hopping term ( t '), using an optimization (or correlated) variational Monte Carlo method. In the trial wave functions, a doublon–holon binding effect is introduced in addition to the onsite Gutzwiller projection. We mainly treat a d -wave singlet state and a projected Fermi sea. In both wave functions, first-order Mott transitions without direct relevance to magnetic orders occur at U = U c , which is approximately the bandwidth, for arbitrary t '/ t . These transitions originate in the binding or unbinding of a doublon to a holon. d -wave SC appears in a narrow range immediately below U c . The robust d -wave superconducting correlation is necessarily accompanied by enhanced antiferromagnetic correlation; the strength of SC decreases, as t '/ t increases.

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Mott Transitions and d-Wave Superconductivity in Half-Filled-Band Hubbard Model on Square Lattice with Geometric Frustration

We investigate superconducting pair correlations in the attractive Hubbard model on a finite square lattice. Our aim is to understand the pronounced size dependence which they display in the weak and intermediate coupling regimes. These size effects originate from the electronic shell structure of finite systems and severely complicate a reliable extrapolation of numerical simulation data from small systems to the thermodynamic limit. To analyze the size effects in detail, we use the BCS approximation, as well as a particle number conserving modification of it and compare the results with those of quantum Monte Carlo simulations. As an application, we explore the possibility of reducing the shell effects in simulation data by changing the shape of the system and the imposed boundary conditions and by making use of the size dependence of corresponding BCS data.

Quantum size effects in the attractive hubbard model

Magnetic properties observed experimentally in the 3d transition‐metal dichalcogenides with the pyrite structure are reviewed and compared with properties expected theoretically for the Hubbard model. As characteristics of electrons in a narrow band, the following are discussed: (1) The temperature induced and field induced local moment in Co(S,Se)2 and (Co,Ni)S2. (2) The metal‐nonmetal transition in NiS2 and its solid solutions. (3) The paramagnetism and antiferromagnetism in the exchange‐enhanced metal Ni(S,Se)2.

Magnetic properties of 3d transition‐metal dichalcogenides with the pyrite structure

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Hiroyuki Shiba

Papers

Thermodynamic Properties of the One-Dimensional Half-Filled-Band Hubbard Model. II Application of the Grand Canonical Method