Journal Article

Efficient simulation of the 2D Hubbard model via Hilbert space-filling curve mapping

Abedi, Ashkan, De Santis, Dario, Giovannetti, Vittorio

2026

Overview

We investigate tensor network simulations of the two-dimensional (2D) 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 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 × 32 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 2D quantum systems beyond the limits accessible with standard approaches.

• Publisher: IOP Publishing
• Subject: Accuracy / Algorithms / Boundary conditions / Correlation / Efficiency / Fractals / Hilbert curve / Hilbert space / hubbard model / Mapping / matrix product states (MPS) / Numerical analysis / Optimization / Physics / Simulation / space-filling curves / tensor network methods / Tensors