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Transformer Variational Wave Functions for Frustrated Quantum Spin Systems.

Luciano Loris Viteritti1, Riccardo Rende2, Federico Becca1

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We introduce the Vision Transformer (ViT) wave function, a novel neural network for quantum systems. This method accurately models complex quantum states using self-attention, simplifying analysis of many-body systems.

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Area of Science:

  • Quantum Many-Body Physics
  • Machine Learning in Physics
  • Computational Quantum Science

Background:

  • The Vision Transformer (ViT) architecture excels in natural language processing and computer vision, utilizing self-attention for long-range correlations.
  • Quantum many-body systems present significant computational challenges due to their complexity and the need to capture intricate correlations.
  • Variational neural network states offer a promising avenue for approximating complex quantum wave functions.

Purpose of the Study:

  • To adapt the Vision Transformer (ViT) architecture for modeling quantum many-body systems.
  • To introduce a new class of variational neural-network states, termed the ViT wave function.
  • To assess the efficacy of the ViT wave function on a benchmark quantum model.

Main Methods:

  • Developed a novel adaptation of the ViT architecture using complex parameters for quantum wave functions.
  • Applied the proposed ViT wave function to the one-dimensional J1-J2 Heisenberg model.
  • Investigated both shallow and deep architectural configurations, focusing on the self-attention mechanism.

Main Results:

  • The ViT wave function achieved excellent accuracy for both gapped and gapless phases of the Heisenberg model.
  • A simplified, shallow ViT architecture with a single self-attention layer proved highly effective.
  • The approach demonstrated the capability to accurately model large quantum systems by combining local and global operations.

Conclusions:

  • The ViT wave function represents a powerful new tool for studying quantum many-body systems.
  • Its success highlights the potential of transformer-based architectures in quantum physics.
  • The method offers a scalable and accurate approach for tackling complex quantum models, including frustrated systems.