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Simulating the Two-Dimensional t−J Model at Finite Doping with Neural Quantum States

Hannah Lange1,2,3,*,†, Annika Böhler1,2,*,‡, Christopher Roth4, and Annabelle Bohrdt5,2

  • *These authors contributed equally to this work.
  • †Contact author: hannah.lange@physik.uni-muenchen.de
  • ‡Contact author: annika.boehler@physik.uni-muenchen.de
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Phys. Rev. Lett. 135, 136504 – Published 24 September, 2025

DOI: https://doi.org/10.1103/rc31-5hl9

Abstract

Simulating large, strongly interacting fermionic systems remains a major challenge for existing numerical methods. In this Letter, we introduce Gutzwiller projected hidden fermion determinant states (G-HFDS) to simulate the strongly interacting limit of the Fermi-Hubbard model, namely the t−J model, across the entire doping regime. We demonstrate that the G-HFDS achieve energies competitive with matrix product states on lattices as large as 10×10 sites while using several orders of magnitude fewer parameters, suggesting the potential for efficient application to even larger system sizes. This remarkable efficiency enables us to probe low-energy physics across the full doping range, providing new insights into the competition between kinetic and magnetic interactions and the nature of emergent quasiparticles. Starting from the low-doping regime, where magnetic polarons dominate the low energy physics, we track their evolution with increasing doping and different next-nearest neighbor hopping amplitudes through analyses of spin and polaron correlation functions as well as the Fermi surface. Our findings demonstrate the potential of determinant-based neural quantum states with an inherent fermionic sign structure, opening the way for simulating large-scale fermionic systems at any particle filling.

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Phys. Rev. Lett. 135, 136504– Published 24 September, 2025
  • Received 22 January 2025
  • Revised 31 July 2025
  • Accepted 27 August 2025
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