Quantum Many-Body Computation
September – December 2025
Professor Zi Yang Meng, The University of Hong Kong
Purpose of the Course:
Computational approaches are playing increasingly important roles in the advances of condensed matter physics and quantum material research, particularly in quantum many-body systems. In recent years, a new trend of research, combining computational methods, such as exact diagonalization, quantum Monte Carlo, tensor network and neural network, and theoretical approaches such as quantum field theory and symmetry analysis, has emerged and enabled scientists to thoroughly, and in an interdisciplinary manner, investigate the highly entangled quantum phases of matter, 2D moiré materials, quantum simulators, etc. Considering these rapid developments and their lack of systematic education to senior undergraduate students, graduate students and researchers in Hong Kong and the GBA area, I have designed this course to cover from basic to advanced topics in quantum many-body computation and theoretical understanding in strongly correlation aspects of quantum materials. I plan to teach the participants basic and live knowledge of modern quantum many-body computation, such that they can apply them into their research works in the corresponding areas.
Time and Place:
Wednesday 1500 -- 1550, 1600 -- 1650, 1700 -- 1750
Room 103, 1/F, Meng Wah Complex, HKU
Content and Materials:
1). Hartree-Fock mean-field theories for Hubbard model and Heisenberg model on different lattices, to understand the various Landau-Ginzburg-Wilson (LGW) types of symmetry-breaking phases and phase transitions;
2). Exact Diagonalization with symmetry and quantum number implemented for quantum spin systems and field theory with topological term, to understand the basics of quantum phases and topological aspects therein;
3). Density Matrix Renormalization Group methods, to understand the entanglement, informational and dynamic aspects of quantum many-body states and their phase transitions;
4). Quantum Monte Carlo algorithms for interacting fermion (Determinant QMC) and spin/boson lattice models (Stochastic Series Expansion QMC) and quantum entanglement measurements, to understand the basic concept of quantum criticality and the unconventional quantum matter beyond LGW paradigm in 2D material and quantum simulator research.
The teaching materials are based on lecture and algorithm notes and codes on the platform-free cloud computing environment prepared by the teacher.