Research Interests
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My research aims to study quantum many-body systems in and out of equilibrium, by developing low-scaling, high-accuracy computational tools.
Why many-body physics?
Understanding real materials at the many-particle level has been increasingly crucial, since for many materials, the many-particle effect plays a central role in determining the electronic, magnetic, optical, and sometimes even mechanical properties. The rapid advancement in the experimental ability to manipulate and probe interacting electrons have opened unprecedented opportunities and challenges for understanding such materials.Beyond the comfort zone of applied mathematics
To study many-body effects, the standard paradigm is to conduct effective single-particle calculations, which transform the original many-body problem into solving a PDE problem in \(\mathbb R^3\). This basic framework is where applied mathematicians usually work in, as tools from numerical PDEs are directly applicable. However, such single-particle theories often fail to describe general many-body phenomena. My research thus focuses on approaches that go beyond the single-particle picture to directly capture many-body correlations. From an applied mathematics perspective, this many-body regime remains highly underexplored.
Interdisciplinary research
I develop methods that can explain, calculate and predict the properties of correlated matters in and out-of-equilibrium. I work at the intersection of applied mathematics, condensed matter physics and quantum chemistry. This interdisciplinary nature has brought me many surprises and joy. Read here for some quotes about this aspect.
Pushing the limit of accessibility of computational methods: low-scaling algorithms
A recurring theme in my research is to develop low-scaling algorithms. Despite the rapid advancement of modern supercomputers, the exponential scaling of many-particle Hilbert spaces quickly outpaces the growth of computing power. It is thus fundamentally important to develop low-scaling algorithms so that we can make the best use of modern high-performance computing resources. This includes various aspects, as illustrated below:
- System-size: to simulate larger systems, we need to develop methods that scales mildly with system size.
- Equilibrium to non-equilibrium: in the recent years, huge advancement in equilibrium calculations has been made. How to extend such success to non-equilibrium settings remains an active research topic.
- Correlation: Systems in weak correlation could be treated with perturbative methods, while strong correlation requires more sophisticated approaches.
