We study the nonequilibrium dynamics of a binary disordered alloy when it is subjected to an interaction quench. Our study uses a nonequilibrium embedding scheme (DMFT+CPA) that combines the capacity of DMFT (dynamical mean field theory) to treat strongly correlated systems and the capacity of CPA (coherent potential approximation) to treat disordered systems, to effectively address the interplay of disorder and interaction for the nonequilibrium system. Our solution is applied on the equilibrium binary disordered and interacting alloy for the calculation of the density of states. This equilibrium density of states shows the modifications of the disorder-driven gap by the interaction and that of the interaction-driven Mott gap by the disorder. Next, we assess the relaxation of the system that is initially in equilibrium at a given temperature, and then abruptly has its interaction strength changed from zero to a finite value at which it is kept constant. The system undergoes a short time transient and then settles into a long-time state in a process that depends in a nontrivial manner on the disorder and interaction strength. In addition, we calculate the effective temperature of the system after it has gone through its initial transient and settled into its long-time state. The long-time effective temperature is increased with increasing final interaction strength. However, for a given final interaction, the final temperature can be tuned by the disorder strength over a broad range, with stronger disorder leading to lower temperature. Altogether, the results illustrate the nontrivial interplay between disorder and interaction for a binary alloy away from equilibrium.
We study the nonequilibrium dynamics of a binary disordered alloy when it is subjected to an interaction quench. Our study uses a nonequilibrium embedding scheme (DMFT+CPA) that combines the capacity of DMFT (dynamical mean field theory) to treat strongly correlated systems and the capacity of CPA (coherent potential approximation) to treat disordered systems, to effectively address the interplay of disorder and interaction for the nonequilibrium system. Our solution is applied on the equilibrium binary disordered and interacting alloy for the calculation of the density of states. This equilibrium density of states shows the modifications of the disorder-driven gap by the interaction and that of the interaction-driven Mott gap by the disorder. Next, we assess the relaxation of the system that is initially in equilibrium at a given temperature, and then abruptly has its interaction strength changed from zero to a finite value at which it is kept constant. The system undergoes a short time transient and then settles into a long-time state in a process that depends in a nontrivial manner on the disorder and interaction strength. In addition, we calculate the effective temperature of the system after it has gone through its initial transient and settled into its long-time state. The long-time effective temperature is increased with increasing final interaction strength. However, for a given final interaction, the final temperature can be tuned by the disorder strength over a broad range, with stronger disorder leading to lower temperature. Altogether, the results illustrate the nontrivial interplay between disorder and interaction for a binary alloy away from equilibrium.
Although most studies of strongly correlated systems away from equilibrium have focused on clean systems, it is well known that disorder may significantly modify observed properties in various nontrivial ways. The nonequilibrium interplay of interaction and disorder in these systems thus requires further investigation. In the present paper, we use the recently developed nonequilibrium DMFT+CPA embedding scheme, that combines both the dynamical mean field theory (DMFT) and the coherent potential approximation (CPA) nonequilibrium extensions, to characterize the relaxation and the thermalization of a disordered interacting system described by the Anderson-Hubbard model under an interaction quench. The system, initially in equilibrium at a given temperature, has the interaction abruptly switched from zero to a finite value at a given time. To investigate the role of disorder, we use our effective medium approach to calculate, for different values of the final interaction and of the disorder strength, the distribution functions as the system evolves in time. This allows us to determine the effective temperature after the quench and to analyze the effects of disorder on the thermalization for various interaction strengths. We find that, for moderate interactions after the interaction quench, disorder can tune the final temperature of the system across a broad range of values with increased disorder strength leading to lower effective temperature.
Correlated, disordered lattice fermion systems out of equilibrium have been understudied, at least in part for lack of tools to study them. The development of a new method, the NE-DMFT+CPA, is explicated, for investigating the properties of these systems. This method combines DMFT and the CPA using the Kadanoff-Baym-Keldysh contour-time formalism to study the dynamics of interacting disordered systems out of equilibrium. The method is detailed, then applied to the case of the Anderson-Hubbard model: first to replicate well-known equilibrium results, then to study the case of the model under the effect of an interaction quench. Here the effect of disorder on the relaxation of the system is studied by the time-dependence of the energies and momentum distribution function, which display the screening of the Coulomb interaction by disorder. It is then used to examine the thermalization of the same system by using the fluctuation-dissipation theorem to extract the distribution function and thereby the effective temperature after relaxation. This allows the characterization of the effect of the interplay of the disorder strength and the Coulomb interaction on the thermalization behavior. It is found that the heating of the system due to the quench is mitigated by stronger disorder. Finally, current progress of the work to apply the method to binary alloy disorder and an interaction ramp is summarized. Binary disorder appears to have the effect of damping the initial transient of the potential energy more strongly than the comparable uniformly-disordered system. The relaxation of the energies under the effect of an interaction ramp suggests that the crossing of the kinetic energies may be affected by the form of the time-dependent interaction.
We present a solution for the nonequilibrium dynamics of an interacting disordered system. The approach adapts the combination of the equilibrium dynamical mean-field theory and the equilibrium coherent potential approximation methods to the nonequilibrium many-body formalism, using the Kadanoff-Baym-Keldysh complex time contour, for the dynamics of interacting disordered systems away from equilibrium. We use our time domain solution to obtain the equilibrium density of states of the disordered interacting system described by the Anderson-Hubbard model, bypassing the necessity for the cumbersome analytical continuation process. We further apply the nonequilibrium solution to the interaction quench problem for an isolated disordered system. Here, the interaction is abruptly changed from zero (noninteracting system) to another constant (finite) value at which it is subsequently kept. We observe via the time dependence of the potential, kinetic, and total energies the effect of disorder on the relaxation of the system as a function of final interaction strength. The real-time approach has the potential to shed light on the fundamental role of disorder in the nonequilibrium dynamics of interacting quantum systems.
Correlated electrons in a binary alloy ${A}_{x}{B}_{1\ensuremath{-}x}$ are investigated within the Hubbard model and dynamical mean-field theory (DMFT). The random energies ${\ensuremath{\epsilon}}_{i}$ have a bimodal probability distribution and an energy separation $\ensuremath{\Delta}.$ We solve the DMFT equations by the numerical renormalization-group method at zero temperature and calculate the spectral density as a function of disorder strength $\ensuremath{\Delta}$ and interaction U at different fillings. For filling factors $\ensuremath{\nu}=x$ or 1+x the lower or upper alloy subband is half filled and the system becomes a Mott insulator at strong interactions, with a correlation gap at the Fermi level. At the metal-insulator transition hysteresis is observed. We also analyze the effective theory in the $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\Delta}}\ensuremath{\infty}$ limit and find good agreement between analytical and numerical results for the critical interaction Uc at which the metal-insulator transition occurs.
Dynamical mean-field theory (DMFT) is a widely used, nonperturbative computational framework for strongly correlated electron systems. This thesis extends DMFT in two directions: treating disorder and higher-order correlators away from equilibrium, and using near-term quantum computers as impurity solvers. In the first part, we develop two methodological advances for the nonequilibrium DMFT treatment of disordered, interacting systems. The first overcomes the central computational bottleneck of the recently developed nonequilibrium DMFT plus coherent potential approximation (DMFT+CPA) by replacing its explicit numerical disorder averaging with an exact analytical integration, exploiting a normalization property of the Schwinger-Keldysh contour; applied to a disorder-and-interaction quench of the Anderson-Hubbard model, this reveals that weak random disorder promotes thermalization. The second demonstrates that the out-of-time-order correlator (OTOC) can be successfully computed within the existing DMFT+CPA framework, by generalizing the Schwinger-Keldysh contour to a double-folded structure; as a proof-of-principle demonstration, weak disorder is found to accelerate the OTOC's decay in the half-filled Anderson-Hubbard model in the intermediate-coupling regime. In the second part, we explore the use of near-term quantum computers as DMFT impurity solvers. A stable real-time DMFT iteration scheme, designed for compatibility with quantum hardware, is first developed and validated classically against the metal-to-insulator transition. A symmetry-adapted variational quantum eigensolver (VQE) is then benchmarked as the Anderson impurity solver for the converged DMFT Hamiltonian, and is found to reproduce ground-state energies accurately and to extract the single-particle Green's function reliably at intermediate to strong coupling, while accurate ground-state energies are shown not to guarantee accurate dynamics at weak coupling, a key challenge for extending such approaches to correlated metals. Together, we demonstrate that DMFT can be methodologically extended to study disordered and interacting systems away from equilibrium, and to incorporate near-term quantum hardware as a genuinely new computational resource to enhance its capabilities.
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.