Simulating quantum matter through lattice field theories

Abstract

Quantum many-body systems are comprised of complex networks of microscopic interactions that work together to produce novel collective phases and phenomena. For strongly-interacting systems, the connection between the underlying atomic-scale behaviour and the resulting emergent observable phenomena is exponentially (and, in practice, infinitely) complicated such that it becomes impossible to fully understand the connection between the physics at the microscopic and macroscopic levels. The most promising theoretical approaches to addressing this infinite complexity utilize microscopic coarse-graining along with powerful computational simulations and strategies. In this thesis, we apply numerical methods to effective lattice models and field theories with the goal of shedding light onto universal critical behaviour and exotic low-temperature phases in condensed matter physics.

We start by exploring universal features of critical non-interacting systems, for which several analytical strategies are readily available for calculating certain observables. We study the behaviour of the system's entanglement for various entangling geometries, and utilize numerical techniques in order to isolate new universal features of Gaussian fixed points, which provide insight into the underlying critical theory's renormalization group flow. We then proceed to examine computational strategies and, in particular, Monte Carlo simulations for studying more general interacting models. We focus on the application of such strategies to the field of high-temperature superconductivity, for which we develop a coarse-grained model, simulate macroscopic observables and compare our results with those of recent experiments. We conclude that lattice field theories together with innovative computational methods offer new perspectives on both universality and emergent phenomena in quantum matter.