UC Santa Barbara

Quantum field theory(QFT), although initially developed nearly a century ago to describe interactions between elementary particles, has proven to be a powerful tool in condensed matter systems, where there are naturally huge collections of degrees of freedom. It enables one to describe collective excitations, such as phonons and magnons, understand phase transitions, predict transport properties, and more recently, study topological phases. After a survey of QFT methodology in modern theoretical condensed matter physics in Chapter 1, the dissertation covers four sets of exotic scenarios to which quantum field theoretical methods can be applied:

In Chapter 2, we study boundary properties of several exotic quantum criticalities, including phase transition between symmetry protected topological(SPT) state, topologically orders and states with spontaneous symmetry breaking. Renormalization group(RG) studies show that in each case the bulk criticality can possibly give rise to new boundary phases and phase transitions.

In Chapter 3, we discuss quantum phase transitions beyond Landau's paradigm and its interaction with Fermi surfaces. In particular, we constructed their underlying field theories that can be studied using controlled perturbative RG approach. We found interesting new fixed points with non-fermi liquid(NFL) behaviors and unusual dynamical critical exponent.

In Chapter 4, field theoretical methods are applied to study strongly correlated physics in Moir e materials, namely, various orbital orders, Chern insulators and NFLs. We also propose new mechanisms for interaction driven metal-to-insulator transitions in transition metal dichalcogenides(TMD) Moir e bilayers that can explain its large critical resistivity.

And finally in Chapter 5, we study an ``avoided" phase transition between a trivially gapped fermionic state and an interaction trivialized fermionic SPT state. We point out that the latter state can still be distinguished from the former one by zeroes of its Green's function.