Continuum limit of gauged tensor network states

• URL: http://arxiv.org/abs/2511.10189v1
• Date: Fri, 14 Nov 2025 01:37:57 GMT
• Title: Continuum limit of gauged tensor network states
• Authors: Gertian Roose, Erez Zohar,
• Abstract summary: We show that the continuum limit of certain types of gauged tensor networks is well defined.<n>This leads to a new class of states that may be helpful for the non-perturbative study of gauge theories directly in the continuum.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: It is well known that all physically relevant states of gauge theories lie in the sectors of the Hilbert space which satisfy the Gauss law. On the lattice, the manifeslty gauge invariant subspace is known to be exactly spanned by gauged tensor networks. In this work, we demonstrate that the continuum limit of certain types of gauged tensor networks is well defined and leads to a new class of states that may be helpful for the non-perturbative study of gauge theories directly in the continuum.

Related papers

• Counting gauge-invariant states with matter fields and finite gauge groups [51.56484100374058]
  We generalize the exact number of gauge-invariant states to include the case of scalar and fermionic matter.<n>Results are relevant for resource estimation and also as a crosscheck when working in a gauge-invariant basis.
  arXiv  Detail & Related papers  (2025-09-02T10:29:28Z)
• A tensor network formulation of Lattice Gauge Theories based only on symmetric tensors [0.0]
  We provide a new PEPS tensor network formulation of gauge-invariant theories based on symmetric elementary tensors.<n>The new formulation can be implemented in numerical simulation using available state-of-the-art tensor network libraries.<n>We show that such a new formulation provides a novel duality transformation between lattice gauge theories and specific sectors of globally invariant systems.
  arXiv  Detail & Related papers  (2024-12-22T10:42:05Z)
• Fermionic tensor network methods [0.0]
  We show how fermionic statistics can be naturally incorporated in tensor networks on arbitrary graphs through the use of graded Hilbert spaces. This formalism allows to use tensor network methods for fermionic lattice systems in a local way, avoiding the need of a Jordan-Wigner transformation or the explicit tracking of leg crossings by swap gates in 2D tensor networks.
  arXiv  Detail & Related papers  (2024-04-22T22:22:05Z)
• Holographic Codes from Hyperinvariant Tensor Networks [70.31754291849292]
  We show that a new class of exact holographic codes, extending the previously proposed hyperinvariant tensor networks into quantum codes, produce the correct boundary correlation functions. This approach yields a dictionary between logical states in the bulk and the critical renormalization group flow of boundary states.
  arXiv  Detail & Related papers  (2023-04-05T20:28:04Z)
• Partial Degeneration of Tensors [1.0369231476008116]
  We study partial degeneration, where one of the local linear maps is constant whereas the others vary along a curve. The existence of partial degenerations gives strong upper bounds on the aided rank of a tensor, which allows one to turn degenerations into restrictions.
  arXiv  Detail & Related papers  (2022-12-28T20:49:16Z)
• 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)
• Wilson Loops and Area Laws in Lattice Gauge Theory Tensor Networks [0.0]
  We study transfer operators of tensor network states in the context of lattice gauge theories. We focus on the Wilson loop - a nonlocal, gauge-invariant observable. Using the symmetry, we show how to handle its contraction, and formulate conditions relating local properties to its decay fashion.
  arXiv  Detail & Related papers  (2021-01-13T19:00:03Z)
• Dimension of Tensor Network varieties [68.8204255655161]
  We determine an upper bound on the dimension of the tensor network variety. A refined upper bound is given in cases relevant for applications such as varieties of matrix product states and projected entangled pairs states.
  arXiv  Detail & Related papers  (2021-01-08T18:24:50Z)
• Scaling limits of lattice quantum fields by wavelets [62.997667081978825]
  The renormalization group is considered as an inductive system of scaling maps between lattice field algebras. We show that the inductive limit of free lattice ground states exists and the limit state extends to the familiar massive continuum free field.
  arXiv  Detail & Related papers  (2020-10-21T16:30:06Z)
• Optimization at the boundary of the tensor network variety [2.1839191255085995]
  tensor network states form a variational ansatz class widely used in the study of quantum many-body systems. Recent work has shown that states on the boundary of this variety can yield more efficient representations for states of physical interest. We show how to optimize over this class in order to find ground states of local Hamiltonians.
  arXiv  Detail & Related papers  (2020-06-30T16:58:55Z)
• Quantum Geometric Confinement and Dynamical Transmission in Grushin Cylinder [68.8204255655161]
  We classify the self-adjoint realisations of the Laplace-Beltrami operator minimally defined on an infinite cylinder. We retrieve those distinguished extensions previously identified in the recent literature, namely the most confining and the most transmitting.
  arXiv  Detail & Related papers  (2020-03-16T11:37:23Z)

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.