ABSTRACT
Andrew J. Millis Department of Physics, Columbia University, 538 West, 120th Street, New York, NY 10027, U.S.A.
An atom or molecule embedded in an infinite host material defines a quantum impurity model (QIM). Exchange with the host causes the impurity to make transitions between different quantum states, leading to a nontrivial dynamics which may be described as a quantum field theory in zero space and one time dimension. QIMs exhibit many phenomena of intrinsic theoretical interest including quantum phase transitions (QPTs). The development over the past 15 years of dynamical mean field theory (DMFT) shows that they also serve as an auxiliary problem from whose solution important information relating to the physics of interacting lattice models can be obtained. Numerical simulation of these models remains a challenging task but the development of diagrammatic Monte Carlo techniques over the last few years has led to significant improvements in efficiency and flexibility. Highly precise results on few-orbital models can be computed and large Hilbert-space multiorbital models are now within reach. This chapter provides an overview of recent developments in quantum Monte Carlo methods and their application to multi-orbital systems. It presents both the weak-coupling approach, which scales favorably with system size and allows the efficient simulation of large impurity clusters, and the strong-coupling approach, which can handle QIMs with strong interactions.
