Efficient Simulation of the 2D Hubbard Model via Hilbert Space-Filling Curve Mapping
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908687576072192 |
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| author | Abedi, Ashkan Giovannetti, Vittorio De Santis, Dario |
| author_facet | Abedi, Ashkan Giovannetti, Vittorio De Santis, Dario |
| contents | We investigate tensor network simulations of the two-dimensional Hubbard model by mapping the lattice onto a one-dimensional chain using space-filling curves. In particular, we focus on the Hilbert curve, whose locality-preserving structure minimizes the range of effective interactions in the mapped model. This enables a more compact matrix product state (MPS) representation compared to conventional snake mapping. Through systematic benchmarks, we show that the Hilbert curve consistently yields lower ground-state energies at fixed bond dimension, with the advantage increasing for larger system sizes and in physically relevant interaction regimes. Our implementation reaches clusters up to $32\times32$ sites with open and periodic boundary conditions, delivering reliable ground-state energies and correlation functions in agreement with established results, but at significantly reduced computational cost. These findings establish space-filling curve mappings, particularly the Hilbert curve, as a powerful tool for extending tensor-network studies of strongly correlated two-dimensional quantum systems beyond the limits accessible with standard approaches. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_02666 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Efficient Simulation of the 2D Hubbard Model via Hilbert Space-Filling Curve Mapping Abedi, Ashkan Giovannetti, Vittorio De Santis, Dario Quantum Physics Quantum Gases Statistical Mechanics Strongly Correlated Electrons Computational Physics We investigate tensor network simulations of the two-dimensional Hubbard model by mapping the lattice onto a one-dimensional chain using space-filling curves. In particular, we focus on the Hilbert curve, whose locality-preserving structure minimizes the range of effective interactions in the mapped model. This enables a more compact matrix product state (MPS) representation compared to conventional snake mapping. Through systematic benchmarks, we show that the Hilbert curve consistently yields lower ground-state energies at fixed bond dimension, with the advantage increasing for larger system sizes and in physically relevant interaction regimes. Our implementation reaches clusters up to $32\times32$ sites with open and periodic boundary conditions, delivering reliable ground-state energies and correlation functions in agreement with established results, but at significantly reduced computational cost. These findings establish space-filling curve mappings, particularly the Hilbert curve, as a powerful tool for extending tensor-network studies of strongly correlated two-dimensional quantum systems beyond the limits accessible with standard approaches. |
| title | Efficient Simulation of the 2D Hubbard Model via Hilbert Space-Filling Curve Mapping |
| topic | Quantum Physics Quantum Gases Statistical Mechanics Strongly Correlated Electrons Computational Physics |
| url | https://arxiv.org/abs/2512.02666 |