Tensor Networks for Lattice Gauge Theories beyond one dimension: a Roadmap

• URL: http://arxiv.org/abs/2407.03058v1
• Date: Wed, 3 Jul 2024 12:30:04 GMT
• Title: Tensor Networks for Lattice Gauge Theories beyond one dimension: a Roadmap
• Authors: Giuseppe Magnifico, Giovanni Cataldi, Marco Rigobello, Peter Majcen, Daniel Jaschke, Pietro Silvi, Simone Montangero,
• Abstract summary: Network methods are a class of numerical tools and algorithms to study many-body quantum systems in and out of equilibrium. They have found significant applications in simulating lattice gauge theories approaching relevant problems in high-energy physics.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Tensor network methods are a class of 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 approaching 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. In this work, we review the state-of-the-art of Tensor Network methods and discuss 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.

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