Emergent and topological phenomena in many-body systems: Quantum spin liquids and beyond

Abstract

Emergence refers to the phenomena in many-body systems not obvious from microscopic details and fundamental laws. In this dissertation, I will present some of the works that study exotic emergent phe- nomena. In the first 2 chapters, one kind of gapless quantum spin liquid(QSL) called Dirac Spin Liquid(DSL) is examined, on its stability, experiment signatures and proximate symmetry breaking phases. Dirac fermions, photons and monopoles emerge in DSL, rendering it a strongly interacting phase, with an emergent symmetry group larger than that of the physical system. We establish DSL as likely a stable phase of matter on triangular/kagome lattices and connect DSL with symmetry-breaking magnetic orders on 2D lattices. Then the focus switches to more conventional insulators, and the issue of electric polarization. A topological response term to electromagnetic fields offers a modern definition for polarization. This also implies on the boundary of an insulator, Luttinger theorem is modified to include bulk polarization effects. Lastly, we study a route towards topological superconductivity from a chiral spin liquid(CSL) and construct a wave-function for superconductors without explicit electron pairing.