UC Santa Barbara

This dissertation is devoted to the theoretical study of strongly correlated quantum many-body systems. The central theme is to understand the universal properties of quantum matter from the perspective of renormalization group (RG) fixed points. The guiding principles are provided by symmetries and ’t Hooft anomalies, which are both preserved under RG flow and serve to constrain physical properties. The main body of this dissertation can be divided into four main parts.

The first part concerns boundary critical phenomena associated with symmetry-protected topological (SPT) phases and unconventional quantum phase transitions. Our results include new stable boundary phases and exotic boundary phase transitions in various dimensions. For example, a continuous Neel-VBS transition can be potentially realized at the 1+1D boundary of a 2+1D SPT state protected by SO(3) symmetry.

The second part is about two strongly correlated Moire materials. (1) The band topology in twisted bilayer graphene (TBG) severely complicates the standard lattice model descriptions. Therefore, we seek an alternative and provide a coupled-wire framework describing the correlated physics in TBG. (2) As for the experimentally observed continuous metal-insulator transition in MoTe2/WSe2 heterobilayer, we provide a theoretical proposal involving charge fractionalization, which potentially explains the observed anomalously large critical resistivity.

The third part concerns exotic metallic states beyond Landau Fermi liquid theory. We study the problem mainly from two approaches. (1) In the perturbative RG approach, we show analytically controlled examples of marginal Fermi liquids involving non-Landau quantum critical points. In addition, we show charge fractionalization naturally leads to the bad metal behavior at low temperatures. (2) The other approach is based on exactly solvable toy models for quantum matter without quasiparticles. We construct a square-lattice model for the strange metal phase and generalize it for non-Fermi liquids with tunable transport scaling.

The fourth part is about generalized symmetries and their ’t Hooft anomalies. (1) We illustrate how to unambiguously characterize generalized symmetries (including higher-form symmetries, categorical symmetries, and subsystem symmetries) at quantum phase transitions. (2) We discuss physical constructions and classifications of SPT states involving higher-form symmetries. Special attention is paid to anomaly constraints for condensed matter systems such as quantum dimer models.