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  • Letter
  • Open Access

Ground-state properties via machine learning quantum constraints

Pei-Lin Zheng*, Si-Jing Du*, and Yi Zhang†

  • International Center for Quantum Materials, Peking University, Beijing 100871, China and School of Physics, Peking University, Beijing 100871, China

  • *P.-L. Zheng and S.-J. Du are responsible for one-dimensional fermion chains and spin chains, respectively, and contributed equally.
  • †frankzhangyi@gmail.com
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Phys. Rev. Research 4, L032043 – Published 22 September, 2022

DOI: https://doi.org/10.1103/PhysRevResearch.4.L032043

Abstract

Ground-state properties are central to our understanding of quantum many-body systems. At first glance, it seems natural and essential to obtain the ground state before analyzing its properties; however, its exponentially large Hilbert space has made such studies costly, if not prohibitive, on sufficiently large system sizes. Here, we propose an alternative strategy based upon the expectation values of an ensemble of operators and the elusive yet vital quantum constraints between them where the search for ground-state properties simply equates to classical constrained minimization. These quantum constraints are generally obtainable via sampling and then machine learning on a large number of systematically consistent quantum many-body states. We showcase our perspective on one-dimensional fermion chains and spin chains for applicability, effectiveness, caveats, and unique advantages especially for strongly correlated systems, thermodynamic-limit systems, property designs, etc.

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Phys. Rev. Research 4, L032043– Published 22 September, 2022
  • Received 11 June 2021
  • Accepted 12 September 2022
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