Yuan Xue Qualifying Exam

Abstract: Entanglement and dynamics play an important role in characterizing quantum many-body phases in both equilibrium and open systems. For example, phases of matter can be classified by long-range entanglement such as topological orders (TO) or short-range entanglement such as symmetry-protected topological (SPT) phases. Moreover, gapped fracton phases constitute a new class of quantum states of matter which connects to topological orders but does not fit easily into existing paradigms. In the first part of the talk [1], we investigate the anisotropic ZN Laplacian model which can describe a family of fracton phases defined on arbitrary graphs. Focusing on representative geometries where the 3D lattices are extensions of 2D square, triangular, honeycomb and Kagome lattices into the third dimension, we study their ground state degeneracies and mobility of excitations, and examine their entanglement renormalization group (ERG) flows.

In the second part, I will move on to the open quantum systems where many notions in the pure states can be generalized to the mixed states. We propose a method to simulate a large class of bilayer Hamiltonians by means of open and monitored dynamics of monolayer systems. The method builds on the standard mapping of density matrices onto pure states of a doubled system. We show that, by suitable engineering of the jump operators and postselection on no-click trajectories for certain jumps, it is possible to emulate low-energy states of any bilayer spin Hamiltonian. Potential strong-to-weak symmetry breaking (SW-SSB) is also studied.