One of the greatest fundamental challenges faced by modern theoretical science is the description of the nonequilibrium dynamics of strongly correlated quantum many-body systems. The essence of the difficulty with strongly correlated physics is that single-body approximations suitable to weak correlation (such as most electronic structure methods) do not work: the size of the Hilbert space needed to obtain accurate results increases exponentially with the system size. However, in the theoretical treatment of ground-state and equilibrium properties, many simplifications occur and a variety of efficient algorithms now exists. For instance, Density Matrix Renormalization Group (DMRG) takes advantage of the fact that in 1D systems, only an exponentially small fraction of the Hilbert space is important for representing low-lying states. Another example is Quantum Monte Carlo (QMC) algorithms, which can access finite temperature (and in certain cases even zero temperature) properties of systems by very efficiently performing propagation in imaginary time.

In nonequilibrium systems, no such simplifications are known to exist, and one is faced with the need to confront the full complexity of the problem. Analytical results and reliable approximations are limited to very specific regimes, and numerically exact results are therefore particularly important. We work on numerically exact solutions of simple toy models for quantum transport, called impurity models. These models let us account for the presence of strong correlations due to electronic interactions and coupling to vibrational degrees of freedom or optical modes. To apply QMC to nonequilibrium impurity models, time propagation must be carried out in real time, a fact which leads to a troublesome dynamical sign problem which severely limits the range of accessible timescales. We have shown that by combining bold-line QMC methods with reduced dynamics techniques, we can sometimes circumvent the dynamical sign problem, allowing us to gain access to slow spin relaxation dynamics within the Kondo regime. Using our recently developed inchworm Monte Carlo methods, we can completely bypass the dynamical sign problem in a wide variety of strongly correlated parameter regimes.

Nonequilibrium effects are particularly important at the nanoscale, since nanosystems are far easier to drive away from equilibrium than their bulk counterparts. Nanoscale and mesoscale physics is particularly challenging, because it deals with systems too big to be accessible to quantum chemistry methods and too small for approximations appropriate to the bulk to be valid. We are exploring DMFT approaches to correlated nanosystems ranging from molecular magnets on surfaces to transition-metal clusters in junctions. Strongly correlated systems in equilibrium display a remarkable variety of electronic phases, and a small change in pressure or temperature can take them across a phase boundary from metallic (or even superconducting) to insulating. We will address nanoscale, nonequilibrium issues: how do these systems respond to currents, laser excitations and rapid changes in external parameters? Can they be controlled?

An almost universal aspect of electronic devices is the presence interfaces. Diodes, transistors and solar cells are all similar in that the key to their operation is the action at the inteface between pairs of different semiconductors. Strongly correlated materials exhibit even more interesting effects at their interfaces: for instance, metallic layers can form where two insulators meet. While similar 2D electron gases can form between semiconductors, here not only carriers donated by dopants participate, and the effects might therefore be expected to be far stronger and richer. We will investigate the dynamical properties of interfaces and their response to nonequilibrium forces.