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<p>Tensor network methods are numerical tools and algorithms to study many-body quantum systems in and out of equilibrium, based on tailored variational wave functions. They have found significant applications in simulating lattice gauge theories that approach relevant problems in high-energy physics. Compared to Monte Carlo methods, they do not suffer from the sign problem, allowing them to explore challenging regimes such as finite chemical potentials and real-time dynamics. Further development is required to tackle fundamental challenges, such as accessing continuum limits or computations of large-scale quantum chromodynamics. This work reviews the state-of-the-art tensor network methods and discusses a possible roadmap for algorithmic development and strategies to enhance their capabilities and extend their applicability to open high-energy problems. We provide tailored estimates of the theoretical and computational resource scaling for attacking large-scale lattice gauge theories.</p><p></p>

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Tensor networks for lattice gauge theories beyond one dimension

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年8月9日

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  • Giuseppe Magnifico,
  • Giovanni Cataldi,
  • Marco Rigobello,
  • Peter Majcen,
  • Daniel Jaschke,
  • Pietro Silvi,
  • Simone Montangero

摘要

Tensor network methods are numerical tools and algorithms to study many-body quantum systems in and out of equilibrium, based on tailored variational wave functions. They have found significant applications in simulating lattice gauge theories that approach relevant problems in high-energy physics. Compared to Monte Carlo methods, they do not suffer from the sign problem, allowing them to explore challenging regimes such as finite chemical potentials and real-time dynamics. Further development is required to tackle fundamental challenges, such as accessing continuum limits or computations of large-scale quantum chromodynamics. This work reviews the state-of-the-art tensor network methods and discusses a possible roadmap for algorithmic development and strategies to enhance their capabilities and extend their applicability to open high-energy problems. We provide tailored estimates of the theoretical and computational resource scaling for attacking large-scale lattice gauge theories.