**题目**: Differential Topology and Ground States of Fermionic Systems

**时间**: 2024年03月20日 10:00

**报告人**: Dr. Haiqing Wei

Quantica Computing, LLC, California

**Abstract：**

This talk touches upon the rudiments of differential topology that are related to the quantum physics of fermionic systems, specifically, the wavefunction nodal structure of a many-fermion ground state. Theoretically, it is an interesting problem in mathematics to determine the nodal topology of the solution to a given differential operator. Practically in computational physics, knowledge of the wavefunction nodal structure bears great importance for fixed-node or constrained path quan tum Monte Carlo, as a trial wavefunction must get the topology right in order to approximate a true ground state.

A well-known conjecture by Ceperley posits that the ground state of any single-species fermionic system has just one positive nodal cell. Its truth has been proved rigorously for fermionic systems without interactions. However, it remains open in the presence of interactions among identical fermions. We will outline a physics-inspired proof for Ceperley's conjecture using the mathematical tools of homotopy and set-valued analytic curves, which strongly reminisce familiar processes and phenomena in physics, including the adiabatic evolution of a quantum system under a slow-varying Hamiltonian, and avoided crossing of energy levels by a perturbation to remove degeneracy.

**Brief CV of Dr. Haiqing Wei:**

Haiqing Wei holds B.Sc. from Peking University and Ph.D. from McGill University. He has been an industrial physicist, worked in various areas of technology, and become a leading expert in the fields of large-scale software development, systems engineering, modeling and simulations, mathematical optimization, image processing, convolutional nonlinear networks, and quantum computing. He is currently a co-founder and CTO of a company specializing in research and development of industrial software. Dr. Wei is also an avid citizen scientist in his spare time, working on fundamental as well as applied physics and mathematics.

**报告地点：**M楼 253会议室

**主 持 人：**胡江平 研究员

**联 系 人：**傅琦（82649469）