Professor Lin Lin

Professor Lin Lin
Department of Mathematics
University of California, Berkeley
Printable Abstract

Finite-size error in quantum chemistry methods for periodic systems

For periodic systems, energies and other observables should be evaluated at the thermodynamic limit (TDL). The ubiquitously present finite-size error is the difference between the TDL value and its finite-sized approximation. We present to our knowledge the first rigorous analysis of finite-size errors in a range of quantum chemistry methods applied to periodic insulating systems, including Hartree-Fock theory, Møller–Plesset perturbation theory, random phase approximation, and coupled-cluster theory. At the core of our approach is the reduction of finite-size error analysis to the study of quadrature errors associated with the trapezoidal rule for singular integrands with certain algebraic singularities. Using this framework, we uncover the origin of the surprising inverse volume scaling behavior observed in periodic coupled-cluster theory calculations. Our analysis also suggests new finite size corrections tech-niques, which have been incorporated into quantum chem-istry software packages such as PySCF and Q-Chem.

Lin Lin

I am a Professor in the Department of Mathematics at UC Berkeley, and a Senior Faculty Scientist in the Mathematics Group at Lawrence Berkeley National Laboratory. My research focuses on solving quantum many-body problems via both classical and quantum algorithms. These algorithms are often valuable across various domains, including quantum chemistry, quantum physics, materials science, and quantum information theory. I am very fortunate to have received the Sloan Research Fellowship (2015), the National Science Foundation CAREER award (2017), the Department of Energy Early Career award (2017), the (inaugural) SIAM Computational Science and Engineering (CSE) early career award (2017), the Presidential Early Career Awards for Scientists and Engineers (PECASE) (2019), the ACM Gordon Bell prize (Team) (2020), and the Simons Investigator in Mathematics award (2021).

Hosted by Professor Jiali Gao