This program will extend and apply a numerical technique developed by the PI and CO-PI by which the properties of a wide range of interacting field theories in low dimensions can be studied in a nonperturbative fashion. The approach takes as input already available data, in the form of spectra together with matrix elements, arising from integrable and conformal field theoretical treatments of a wide class of strongly interacting zero and one dimensional systems. Using this as a foundation, more complicated field theories, built by either perturbing or coupling together such systems, are analyzed numerically through a controlled truncation of the Hilbert space guided by a renormalization group procedure. This is the renormalization group improved truncated spectrum approach (RGTSA). The strongest interactions are taken into account at the very start. Using it one can study arbitrary perturbations of 1+1 dimensional integrable and conformal field theories as well as study large arrays of coupled one-dimensional field theories, permitting the extension of the approach to 2+1 dimensions. The numerical renormalization group technique borrows ideas from the study of quantum impurity problems and density matrix renormalization group approaches to one dimensional lattice models. This technique is sufficiently versatile to extract the spectrum, correlation functions and non-equilibrium phenomena such as the dynamics following a quantum quench.
This technique is able to characterize the properties of real materials. As a proof of principle of the technique, the excitonic spectrum of semi-conducting carbon nanotubes has been studied and it has been shown that the modeling well describes experimental data. This technique will be used to study the optical properties of hybrid nanosystems with the aim of better understanding this hybrid's potential as a solar energy device. Two graduate students will receive extensive training in low dimensional quantum field theories as well as their application in condensed matter settings. They will conduct original research and develop theoretical methods with cross-field applicability. The results will be presented in journals and through seminars, colloquia, and conference presentations.
