Theoretical analyses of strongly entangled low-temperature quantum spin systems in one and two dimensions

Abstract

In this thesis, I provide a record of my work on two projects. The first project focuses on the magnetic physics of the spin-liquid candidate material Ca₁₀Cr₇O₂₈. Using methods including exact diagonalization, Thermal Pure Quantum States, and high-temperature expansions, I provide evidence that the model proposed by Balz et al. [Phys. Rev. B 95, 174414 (2017)] is significantly incomplete as a description of the magnetism of this material, with reference to the zero-field specific heat capacity. I then provide an account of my work to date on constructing an improved model --- in particular, I motivate the addition of anisotropic terms. The second project in this thesis seeks to extend the utility of a method called the path integral over tensor networks. Studying the staggered XX spin chain, I present my progress in deriving an effective field theory, identifying zero-energy edge modes, and calculating fluctuation corrections to saddle-point energies. The aim of these calculations is to explore how the path integral over tensor networks method makes the topological physics of this model accessible. As it stands, my work is inconclusive in this regard, and I discuss some possible issues with my analysis.

Date of Award	2 Dec 2025
Original language	English
Awarding Institution	University of St Andrews
Supervisor	Bernd Braunecker (Supervisor) & Chris Hooley (Supervisor)