UC Santa Barbara

Over the last several decades, two theoretical tools have been indispensable in the field of statistical physics. Spontaneous symmetry breaking has allowed for the description of systems which exhibit second order phase transitions, while the eigenstate thermalization hypothesis has provided a theoretical framework for understanding how isolated quantum many-body systems come to thermal equilibrium. In this dissertation, we will explore the compatibility of these two paradigms of theoretical physics.

We will begin with a brief introduction to the relevant topics discussed in the main body of the dissertation, along with a brief overview of the numerical tools used in the subsequent investigations.

Following this, we will numerically explore the compatibility between spontaneous symmetry breaking and eigenstate thermalization through a sequence of papers which have been previously published by myself and a collection of other authors. We will study the compatibility of these two theoretical frameworks through an exact diagonalization and Quantum Monte Carlo study of the Transverse-Field Ising model, a quantum non-integrable system which, we argue, displays both spontaneous symmetry breaking and eigenstate thermalization.

Following this exposition, we will briefly comment on several corollaries which follow from these previously published papers, some of which we are currently preparing to incorporate into future publications. These corollaries largely focus on the subject of time evolution in quantum systems which display both spontaneous symmetry breaking and eigenstate thermalization, as well as the possibility that individual eigenstates of such systems may contain information about the critical behaviour of the corresponding finite-temperature phase transition.