Research in the Particle Theory group
At nonzero baryon density, the principal numerical technique of lattice field theory, importance sampling using Monte Carlo methods, cannot be applied, since the weight in the partition function is not positive definite. As a result the QCD phase diagram has not yet been determined, making it one of the outstanding problems in the theory of the strong interactions under extreme conditions, relevant for heavy-ion collisions at low baryon density and neutron and quark stars at high density.
We investigate this so-called sign problem using a number of approaches. Two-colour QCD is the simplest gauge theory in which cold dense baryonic matter induced at nonzero chemical potential can be studied using orthodox lattice simulation techniques, since the sign problem is absent. Here we have studied the phase diagram and identified a quarkyonic phase, in which the matter remains confined but the scaling of thermodynamic quantities such as pressure and density is that of a degenerate quark system.
A possible way to handle the sign problem is to extract the density of the states with a Monte Carlo method (which involves sampling with a real measure) and then use this numerically determined quantity to compute the partition function of the original system by a semi-analytical integration. With this method, the density of states can be accurately obtained over several order of magnitude. This is a crucial prerequisite to handle precise numerical cancellations in the partition function. The feasibility of this approach to tackle severe sign problems in realistic systems is currently under investigation.
For QCD a radically different approach is based on the complex Langevin equation, which does not rely on importance sampling and has been shown to be able to solve severe sign problems in four-dimensional quantum field theories at nonzero density. In our ongoing programme, this approach can now be applied to nonabelian gauge theories, using the method of gauge cooling. We are studying QCD with a finite quark density as well as QCD with a nonzero theta-term.