Assistant Professor of Physics,
Room 312, McCullough Bldg.
At this moment I am mainly interested in three related fields in condensed matter physics---topological phenomena, quantum entanglement and holographic duality.
Topological phenomena are the phenomena which are determined by some topological structure in the physical system, which are thus usually universal and robust against perturbations. For example, two famous topological phenomena are the flux quantization in superconductors and Hall conductance quantization in the Quantum Hall states. Recent discovery of topological insulators and topological superconductors in different symmetry classes bring the opportunity to study a large family of new topological phenomena. For example the three-dimensional topological insulator provides a condensed matter realization of the important theoretical concepts in high energy physics such as ”\theta-vacuum” and “axion”. The interplay of topological insulators and superconductors with conventional phases of matter such as ferromagnets and superconductors lead to richer topological phenomena. For an intuitive introduction to topological insulators, see Qi and Zhang, Physics Today Jan 2010.
Quantum entanglement is the unique feature of quantum mechanics, which is essential for quantum information and quantum computation. The understanding of quantum entanglement provides a new probe to the physical properties of the many-body systems compared to the conventional response properties such as conductivity, spin susceptibility, etc. On the other hand, more systematical understanding of quantum entanglement in many-body systems may also lead to breakthrough in building a quantum computer. It is far more difficult to study entanglement properties in many-body systems compared to few-body systems. There are a lot of open questions for which the answer is not known or only known for specific systems. For example, what is the general relation between entanglement properties and other physical observables in a given system? What is the relation between quantum entanglement and topological states of matter? Besides the known description of entanglement such as von Neumann entropy, what other measure can be defined to provide more refined characterization of entanglement? I am pursuing these directions. For a recent work I did along this line, click here.
Holographic duality uncovers an intrinsic relationship between dimensional gravitational theories and dimensional non-gravitational theories such as CFT’s. This duality is often referred to as AdS/CFT correspondence when the d-dimensional non-gravitational theory is a conformal field theory (CFT). Each field in the bulk gravity theory corresponds to a local operator in the boundary theory, in the sense that all correlation functions in the large N limit are determined by the classical action of the bulk theory as a functional of the boundary conditions. The extra dimension in the (d + 1) dimensional gravity theory can be interpreted as corresponding to energy scale in the CFT. In a suitable coordinate choice, the scaling dimension of an operator is determined by the mass of the corresponding bulk field. I am interested in understanding holography starting from the boundary quantum field theory (a condensed matter system) rather than the string theory. I am interested in developing a new framework called “functional holographic duality” which takes a generic boundary theory as the starting point and exactly constructs the dual bulk theory. I gave a talk at KITP about this subject.