Efficient Simulation of the 2D Hubbard Model via Hilbert Space-Filling Curve Mapping

• URL: http://arxiv.org/abs/2512.02666v1
• Date: Tue, 02 Dec 2025 11:44:12 GMT
• Title: Efficient Simulation of the 2D Hubbard Model via Hilbert Space-Filling Curve Mapping
• Authors: Ashkan Abedi, Vittorio Giovannetti, Dario De Santis,
• Abstract summary: We map the lattice onto a one-dimensional chain using space-filling curves.<n>We show that the Hilbert curve consistently yields lower ground-state energies at fixed bond dimension.<n>These findings establish space-filling curve mappings as a powerful tool for extending tensor-network studies of strongly correlated two-dimensional quantum systems.
• Score: 0.764671395172401
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

Related papers

• Brep2Shape: Boundary and Shape Representation Alignment via Self-Supervised Transformers [46.87466345672103]
  Boundary representation (B-rep) is the industry standard for computer-aided design (CAD)<n>While deep learning shows promise in processing B-rep models, existing methods suffer from a representation gap.<n>We introduce Brep2Shape, a novel self-supervised pre-training method designed to align abstract boundary representations with intuitive shape representations.
  arXiv  Detail & Related papers  (2026-02-07T08:00:47Z)
• Tensor network simulations of quasi-GPDs in the massive Schwinger model [0.0]
  Generalized Parton Distribution functions encode the internal structure of hadrons in terms of quark and gluon degrees of freedom.<n>We present the first nonperturbative study of quasi-GPDs in the massive Schwinger model.
  arXiv  Detail & Related papers  (2025-11-21T20:06:09Z)
• Hybrid Quantum-Classical Eigensolver with Real-Space Sampling and Symmetric Subspace Measurements [7.924603170890832]
  We propose a hybrid quantum-classical eigensolver to address the computational challenges of strongly correlated quantum many-body systems.<n>Our approach combines real-space sampling of tensor-network-bridged quantum circuits with symmetric subspace measurements.
  arXiv  Detail & Related papers  (2025-10-22T04:03:40Z)
• Gaussian Entanglement Measure: Applications to Multipartite Entanglement of Graph States and Bosonic Field Theory [50.24983453990065]
  An entanglement measure based on the Fubini-Study metric has been recently introduced by Cocchiarella and co-workers. We present the Gaussian Entanglement Measure (GEM), a generalization of geometric entanglement measure for multimode Gaussian states. By providing a computable multipartite entanglement measure for systems with a large number of degrees of freedom, we show that our definition can be used to obtain insights into a free bosonic field theory.
  arXiv  Detail & Related papers  (2024-01-31T15:50:50Z)
• Shape And Structure Preserving Differential Privacy [70.08490462870144]
  We show how the gradient of the squared distance function offers better control over sensitivity than the Laplace mechanism. We also show how using the gradient of the squared distance function offers better control over sensitivity than the Laplace mechanism.
  arXiv  Detail & Related papers  (2022-09-21T18:14:38Z)
• Rethinking the Zigzag Flattening for Image Reading [48.976491898131265]
  We investigate the Hilbert fractal flattening (HF) as another method for sequence ordering in computer vision. The HF has proven to be superior to other curves in maintaining spatial locality. It can be easily plugged into most deep neural networks (DNNs)
  arXiv  Detail & Related papers  (2022-02-21T13:53:04Z)
• Geodesic Quantum Walks [0.0]
  We propose a new family of discrete-spacetime quantum walks capable to propagate on any arbitrary triangulations. We extend and generalize the duality principle introduced by one of the authors, linking continuous local deformations of a given triangulation and the inhomogeneity of the local unitaries that guide the quantum walker.
  arXiv  Detail & Related papers  (2022-02-21T13:52:19Z)
• Convex Analysis of the Mean Field Langevin Dynamics [49.66486092259375]
  convergence rate analysis of the mean field Langevin dynamics is presented. $p_q$ associated with the dynamics allows us to develop a convergence theory parallel to classical results in convex optimization.
  arXiv  Detail & Related papers  (2022-01-25T17:13:56Z)
• Boundary theories of critical matchgate tensor networks [59.433172590351234]
  Key aspects of the AdS/CFT correspondence can be captured in terms of tensor network models on hyperbolic lattices. For tensors fulfilling the matchgate constraint, these have previously been shown to produce disordered boundary states. We show that these Hamiltonians exhibit multi-scale quasiperiodic symmetries captured by an analytical toy model.
  arXiv  Detail & Related papers  (2021-10-06T18:00:03Z)
• Hilbert curve vs Hilbert space: exploiting fractal 2D covering to increase tensor network efficiency [1.2314765641075438]
  We present a novel mapping for studying 2D many-body quantum systems. In particular, we address the problem of choosing an efficient mapping from the 2D lattice to a 1D chain. We show that the locality-preserving properties of the Hilbert curve leads to a clear improvement of numerical precision.
  arXiv  Detail & Related papers  (2021-05-05T18:00:02Z)
• Efficient and Flexible Approach to Simulate Low-Dimensional Quantum Lattice Models with Large Local Hilbert Spaces [0.08594140167290096]
  We introduce a mapping that allows to construct artificial $U(1)$ symmetries for any type of lattice model. Exploiting the generated symmetries, numerical expenses that are related to the local degrees of freedom decrease significantly. Our findings motivate an intuitive physical picture of the truncations occurring in typical algorithms.
  arXiv  Detail & Related papers  (2020-08-19T14:13:56Z)
• Quantum anomalous Hall phase in synthetic bilayers via twistless twistronics [58.720142291102135]
  We propose quantum simulators of "twistronic-like" physics based on ultracold atoms and syntheticdimensions. We show that our system exhibits topologicalband structures under appropriate conditions.
  arXiv  Detail & Related papers  (2020-08-06T19:58:05Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.