Non-perturbative Methods of QFTs
The research interest of this group lies in the study of systems in particle and condensed matter physics whose behavior is dominated by the collective motion of a large number of degrees of freedom. The basic theoretical methods we use are quantum field theories and renormalization group. The technical tools applied are both analytic (like chiral perturbation theory, large-N expansion and Bethe-Ansatz) and numerical.
A large part of our recent research is concentrated on constructing, testing and applying the fixed-point (classically perfect) QCD action. The glueball spectrum, static quark potential and the finite temperature deconfining phase transition was studied in the gauge sector. The fixed point Dirac operator has several theoretically attractive properties, among others it satisfies the Ginsparg-Wilson relation. Its construction is a running project.
Another direction followed is the search for efficient (cluster) algorithms to simulate strongly correlated, or frustrated systems. These algorithms, among others, made it possible to produce high precision results on 2+1 dimensional quantum antiferromagnets which could be confronted with our analytic predictions.
Most aspects of asymptotically free theories are non-perturbative and the behavior of such systems might run against intuition, or predictions which are valid in every order of perturbation theory. We are involved in high precision numerical simulations in 2-dimensional systems to clarify the approach to the continuum limit and other poorly understood aspects of these models.