Hamiltonian Lattice Gauge Theories: emergent properties from Tensor Network methods
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909608320172032 |
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| author | Cataldi, Giovanni |
| author_facet | Cataldi, Giovanni |
| contents | This thesis develops advanced Tensor Network (TN) methods to address Hamiltonian Lattice Gauge Theories (LGTs), overcoming limitations in real-time dynamics and finite-density regimes. A novel dressed-site formalism is introduced, enabling efficient truncation of gauge fields while preserving gauge invariance for both Abelian and non-Abelian theories. This formalism is successfully applied to SU(2) Yang-Mills LGTs in two dimensions, providing the first TN simulations of this system and revealing critical aspects of its phase diagram and non-equilibrium behavior, such as a Quantum Many-Body (QMB) scarring dynamics. A generalization of the dressed-site formalism is proposed through a new fermion-to-qubit mapping for general lattice fermion theories, revealing powerful for classical and quantum simulations. Numerical innovations, including the use of optimal space-filling curves such as the Hilbert curve to preserve locality in high-dimensional simulations, further enhance the efficiency of these methods. Together with high-performance computing techniques, these advances open current and future development pathways toward optimized, efficient, and faster simulations on scales comparable to Monte Carlo state-of-the-art. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_11115 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hamiltonian Lattice Gauge Theories: emergent properties from Tensor Network methods Cataldi, Giovanni High Energy Physics - Lattice Strongly Correlated Electrons Computational Physics Quantum Physics This thesis develops advanced Tensor Network (TN) methods to address Hamiltonian Lattice Gauge Theories (LGTs), overcoming limitations in real-time dynamics and finite-density regimes. A novel dressed-site formalism is introduced, enabling efficient truncation of gauge fields while preserving gauge invariance for both Abelian and non-Abelian theories. This formalism is successfully applied to SU(2) Yang-Mills LGTs in two dimensions, providing the first TN simulations of this system and revealing critical aspects of its phase diagram and non-equilibrium behavior, such as a Quantum Many-Body (QMB) scarring dynamics. A generalization of the dressed-site formalism is proposed through a new fermion-to-qubit mapping for general lattice fermion theories, revealing powerful for classical and quantum simulations. Numerical innovations, including the use of optimal space-filling curves such as the Hilbert curve to preserve locality in high-dimensional simulations, further enhance the efficiency of these methods. Together with high-performance computing techniques, these advances open current and future development pathways toward optimized, efficient, and faster simulations on scales comparable to Monte Carlo state-of-the-art. |
| title | Hamiltonian Lattice Gauge Theories: emergent properties from Tensor Network methods |
| topic | High Energy Physics - Lattice Strongly Correlated Electrons Computational Physics Quantum Physics |
| url | https://arxiv.org/abs/2501.11115 |