Mid-Term Report Summary - QFTCMPS (Quantum field theory, the variational principle, and continuous matrix product states)
Despite the simplicity of the microscopic physical laws of nature, the emergent macroscopic world exhibits a striking diversity of physical phenomena. The traditional tools we use to understand these phenomena have been based either on perturbation theory, where a small parameter is identified allowing us to relate our equations to an exactly solvable case, or Monte Carlo sampling, where computers are used to approximate the solution to the equations describing the microscopic physical laws. We now understand that these mature approaches are insufficient for the task of understanding the macroscopic world and nonperturbative tools such as instantons and the AdS/CFT correspondence of string theory are necessary to go further. Recently, insights from quantum information theory have merged with traditional methods in condensed matter theory to produce a new suite of nonperturbative tools called tensor network states. These tools have had great success in the study of strongly correlated quantum spin lattice systems -- systems which have eluded more traditional approaches such as perturbation theory and Monte Carlo sampling. The objective of this project is to graduate these discrete quantum-information inspired methods to the continuous realm of quantum fields describing the degrees of freedom featuring in the fundamental equations of nature. To achieve this goal we've worked out a systematic way to take the continuous limit of a tensor network state -- an object describing the state of a discrete lattice of quantum systems -- to produce a continuous tensor network, yielding an efficient representation of the nonperturbative physics of a quantum field. We've also applied these states to learn about the counterintuitive properties of strongly interacting quantum fields giving us new insight into phenomena as diverse as Bose-Einstein condensation through to the scattering of fundamental particles, and on to the description of the strange properties of light emerging from tiny cavities.