Diagonal Isometric Form for Tensor Product States in Two Dimensions

• URL: http://arxiv.org/abs/2507.08080v1
• Date: Thu, 10 Jul 2025 18:00:03 GMT
• Title: Diagonal Isometric Form for Tensor Product States in Two Dimensions
• Authors: Benjamin Sappler, Masataka Kawano, Michael P Zaletel, Frank Pollmann,
• Abstract summary: We introduce an alternative isometric form for isoTPS by incorporating auxiliary tensors to represent the decity hypersurface.<n>Our results demonstrate that isoTPS can efficiently capture the entanglement structure of two-dimensional area law states.<n>Our isoTPS formulation further allows for a natural extension to different lattice geometries, such as the honeycomb or kagome latice.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Isometric tensor product states (isoTPS) generalize the isometric form of the one-dimensional matrix product states (MPS) to tensor networks in two and higher dimensions. Here, we introduce an alternative isometric form for isoTPS by incorporating auxiliary tensors to represent the orthogonality hypersurface. We implement the time evolving block decimation (TEBD) algorithm on this new isometric form and benchmark the method by computing ground states and the real time evolution of the transverse field Ising model in two dimensions on large square lattices of up to 1250 sites. Our results demonstrate that isoTPS can efficiently capture the entanglement structure of two-dimensional area law states. The short-time dynamics is also accurately reproduced even at the critical point. Our isoTPS formulation further allows for a natural extension to different lattice geometries, such as the honeycomb or kagome latice.

Related papers

• Push-Forward Signed Distance Functions enable interpretable and robust continuous shape quantification [1.433758865948252]
  Push-Forward Signed Morphometric (PF-SDM) is a novel method for shape quantification in biomedical imaging. PF-SDM effectively captures the geometric properties of shapes, including their topological skeletons and symmetries.
  arXiv  Detail & Related papers  (2024-10-28T13:28:21Z)
• Geometric Trajectory Diffusion Models [58.853975433383326]
  Generative models have shown great promise in generating 3D geometric systems. Existing approaches only operate on static structures, neglecting the fact that physical systems are always dynamic in nature. We propose geometric trajectory diffusion models (GeoTDM), the first diffusion model for modeling the temporal distribution of 3D geometric trajectories.
  arXiv  Detail & Related papers  (2024-10-16T20:36:41Z)
• On Conformal Isometry of Grid Cells: Learning Distance-Preserving Position Embedding [45.67079714578615]
  We investigate the conformal isometry hypothesis as a potential explanation for the hexagonal periodic patterns in grid cell response maps.<n>We conduct numerical experiments to show that this hypothesis leads to the hexagonal grid firing patterns by learning maximally distance-preserving position embedding.
  arXiv  Detail & Related papers  (2024-05-27T06:31:39Z)
• A Hitchhiker's Guide to Geometric GNNs for 3D Atomic Systems [87.30652640973317]
  Recent advances in computational modelling of atomic systems represent them as geometric graphs with atoms embedded as nodes in 3D Euclidean space. Geometric Graph Neural Networks have emerged as the preferred machine learning architecture powering applications ranging from protein structure prediction to molecular simulations and material generation. This paper provides a comprehensive and self-contained overview of the field of Geometric GNNs for 3D atomic systems.
  arXiv  Detail & Related papers  (2023-12-12T18:44:19Z)
• Two dimensional quantum lattice models via mode optimized hybrid CPU-GPU density matrix renormalization group method [0.0]
  We present a hybrid numerical approach to simulate quantum many body problems on two spatial dimensional quantum lattice models. We demonstrate for the two dimensional spinless fermion model and for the Hubbard model on torus geometry that several orders of magnitude in computational time can be saved.
  arXiv  Detail & Related papers  (2023-11-23T17:07:47Z)
• Efficient Representation of Minimally Entangled Typical Thermal States in two dimensions via Projected Entangled Pair States [0.0]
  The Minimally Entangled Typical Thermal States (METTS) are an ensemble of pure states, equivalent to the Gibbs thermal state, that can be efficiently represented by tensor networks. In this article, we use the Projected Entangled Pair States (PEPS) ansatz as to represent METTS on a two-dimensional (2D) lattice. Our analysis reveals that PEPS-METTS achieves accurate long-range correlations with significantly lower bond dimensions.
  arXiv  Detail & Related papers  (2023-10-12T17:23:55Z)
• Geometric Neural Diffusion Processes [55.891428654434634]
  We extend the framework of diffusion models to incorporate a series of geometric priors in infinite-dimension modelling. We show that with these conditions, the generative functional model admits the same symmetry.
  arXiv  Detail & Related papers  (2023-07-11T16:51:38Z)
• Two Dimensional Isometric Tensor Networks on an Infinite Strip [1.2569180784533303]
  We introduce the class ofisoTNS (isoTNS) for efficient simulation of 2D systems on finite square lattices. We iteratively transform an infinite MPS representation of a 2D quantum state into a strip isoTNS and investigate the entanglement properties of the resulting state. Finally, we introduce an infinite time-evolving block decimation algorithm (iTEBDsuperscript2) and use it to approximate the ground state of the 2D transverse field Ising model on lattices of infinite strip geometry.
  arXiv  Detail & Related papers  (2022-11-25T19:00:06Z)
• Ternary unitary quantum lattice models and circuits in $2 + 1$ dimensions [0.0]
  We extend the concept of dual unitary quantum gates to quantum lattice models in $2 + 1$ dimensions. We study ternary unitary four-particle gates, which are unitary in time and both spatial dimensions.
  arXiv  Detail & Related papers  (2022-06-03T10:53:49Z)
• Efficient Simulation of Dynamics in Two-Dimensional Quantum Spin Systems with Isometric Tensor Networks [0.0]
  We investigate the computational power of the recently introduced class of isometric tensor network states (isoTNSs) We discuss several technical details regarding the implementation of isoTNSs-based algorithms and compare different disentanglers. We compute the dynamical spin structure factor of 2D quantum spin systems for two paradigmatic models.
  arXiv  Detail & Related papers  (2021-12-15T19:00:05Z)
• 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)
• Improving Metric Dimensionality Reduction with Distributed Topology [68.8204255655161]
  DIPOLE is a dimensionality-reduction post-processing step that corrects an initial embedding by minimizing a loss functional with both a local, metric term and a global, topological term. We observe that DIPOLE outperforms popular methods like UMAP, t-SNE, and Isomap on a number of popular datasets.
  arXiv  Detail & Related papers  (2021-06-14T17:19:44Z)
• Primal-Dual Mesh Convolutional Neural Networks [62.165239866312334]
  We propose a primal-dual framework drawn from the graph-neural-network literature to triangle meshes. Our method takes features for both edges and faces of a 3D mesh as input and dynamically aggregates them. We provide theoretical insights of our approach using tools from the mesh-simplification literature.
  arXiv  Detail & Related papers  (2020-10-23T14:49:02Z)

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.