Research Field

Topological Quantum Phases of Matter

Topological quantum matter represents a novel class of quantum states in many-body systems whose properties are determined by patterns of quantum entanglement. Unlike conventional phases of matter, they cannot be characterized by local physical observables but instead require a global topological description. The discovery of the fractional quantum Hall effect in the 1980s provided the first experimental evidence for such exotic quantum states. In 2016, the Nobel Prize in Physics was awarded to three physicists for their theoretical discoveries of topological phases of matter and topological phase transitions.

In recent years, the rapid development of quantum simulation platforms—such as superconducting qubits, trapped ions, and Rydberg atoms—has enabled the experimental realization and detection of various topological quantum states. The study of topological quantum matter not only advances the fundamental understanding of condensed matter physics, but also provides a promising foundation for quantum technologies, including quantum information storage, quantum error correction, and topological quantum computation.

Tensor Network States

Tensor network methods provide powerful theoretical and numerical tools for studying quantum many-body systems. They offer an efficient representation of quantum states with complex entanglement structures and significantly reduce the exponential computational complexity typically associated with many-body problems. The density matrix renormalization group (DMRG) is one of the most successful and widely used tensor network algorithms.

In recent years, tensor network methods have found broad applications in condensed matter physics, quantum information science, quantum chemistry, and machine learning. My research employs various tensor network algorithms to investigate complex quantum many-body systems, with a particular focus on the numerical simulation and physical characterization of topological quantum states and their phase transitions.

Generalized Symmetry and Topological Order Parameters

Symmetry is one of the most fundamental concepts in modern physics. In condensed matter and statistical physics, the classical theoretical framework for understanding phases and phase transitions is Landau’s theory of spontaneous symmetry breaking, which characterizes different phases through local order parameters. However, certain quantum phases—such as topological phases—cannot be described within this traditional framework.

To understand these phenomena, it is necessary to introduce a more general concept of symmetry, known as generalized symmetry, and to develop new theoretical frameworks.

Order parameters play a central role in detecting spontaneous symmetry breaking within Landau theory. Similarly, in topological quantum matter, one aims to construct topological order parameters based on generalized symmetries to characterize topological phases and their phase transitions, thereby exploring possible extensions of the traditional Landau paradigm.