NCTS Math-Phys Machine Learning Seminar

Title: Exploring Quantum Many-Body Problems by Random Sampling Neural Networks and Self-Supervised Learning.
Start Date/Time: 2022-03-21 / 12:00 (Taipei time)
End Date/Time: 2022-03-21 / 13:00
Speaker: Prof. Daw-Wei Wang (Phys, NTHU)
Venue: Cosmology Hall 4F Lecture Hall, NTU / R521, 5F, 2nd General Building, NTHU.
Host: Prof. Po-Chung Chen (NTHU) / Jiunn-Wei Chen (NTU)

Venue1: Cosmology Hall 4F Lecture Hall, NTU.
Venue2: R521, 5F, 2nd General Building, NTHU.
Online Zoom [Registration] is required
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Abstract: The eigenvalue problem and the ground state properties of quantum many-body systems is a fundamental and challenging subject in condensed-matter physics because the dimension of the Hilbert space grows exponentially as the system size increases. Here we propose a general numerical method, random sampling neural networks (RSNNs), to utilize the pattern recognition technique for the random sampling matrix elements of an interacting many-body system via a self-supervised learning approach. Several exactly solvable one-dimensional models are tested with pretty high accuracy (>96%) for the energy spectra, magnetization, and critical exponents, etc. in the strongly correlated regime [1]. We further apply such a self-supervised learning method for the identification of topological phase transitions using time-of-fight images in ultracold atoms. Different from the conventional supervised learning approach, where the predicted phase transition point is sensitive to the training region [2]. our results demonstrate a robust identification in various 1D and 2D exactly solvable models. As a result, our self-supervised approach should be a very general and reliable method for quantum many-body systems even without a priori knowledge of the solution. If time is allowed, we will present our recent works for the application in long-time dynamics of a quantum many-body system.

[1] Chen-Yu Liu, Daw-Wei Wang, Phys. Rev. B 103, 205103 (2021).
[2] Chi-Ting Ho and Daw-Wei Wang, New J. Phys. 23 083021 (2021).