Wider Applications of Lattice Field Theory

Quantum field theory is one of the most successful, and widely used, approaches in theoretical physics however, in some cases the mathematical equations are not solvable using a pen and paper. One possible first-principle numerical technique is lattice field theory, in which the continuous dimensions of space and time are restricted to a fixed grid of points with links between them. In this way a system can be modelled using a computer, with increasing precision as the number of points on the grid is increased. This method has been widely used to investigate quantum chromodynamics, the theory of the strong nuclear force that governs the interactions between quarks, which is not analytically solvable due to the strength of the interactions. Lattice field theory may also be used to investigate the behaviour of many body systems, such as graphene, which is relevant in condensed matter physics. Increasingly lattice field theory is being used to investigate the behaviour of beyond the standard model physics, for example, models which include supersymmetry as well as matrix models of string theory such as the Banks-Fischler-Shenker-Susskind model. One area of particular interest is quantum chaos. Classically chaos is defined by the paths of initially close states separating from one another at an exponential rate. This behaviour can also be observed in quantum systems and plays a key role in the thermalization of many body systems, such as the quark-gluon plasma produced during collisions of heavy ions. With black holes being maximally chaotic quantum systems, studies of quantum chaos might also shed light on the theory of quantum gravity. In this project, we plan to study the emergence of nearly maximal quantum chaos in many-body quantum systems. Such systems in the regime of maximal chaos will provide us with microscopic models for black-hole-like physics. In particular, we plan to develop methods for the numerical extraction of thermalization rates (largest Lyapunov exponents) from the results of Monte-Carlo simulations in Euclidean time. We further plan to apply these methods to study the temperature dependence of Lyapunov exponents in gauge theories of strong interactions. In addition to this we will look to employ lattice field theory to a variety of other models, including continuing work that I collaborated on previously which used lattice field theory to demonstrate that the onset of chiral symmetry breaking and the Gross-Witten-Wadia transition, between confinement and partial confinement, coincide in the Eguchi-Kawai model.