Entanglement Sum Rule from Higher-Form Symmetries

• URL: http://arxiv.org/abs/2510.17317v2
• Date: Wed, 22 Oct 2025 11:28:52 GMT
• Title: Entanglement Sum Rule from Higher-Form Symmetries
• Authors: Pei-Yao Liu,
• Abstract summary: We prove an entanglement sum rule for $(d-1)$-dimensional quantum lattice models with finite abelian higher-form symmetries.<n>The framework explains and generalizes known examples in fermion-$mathbbZ$ gauge theory.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We prove an entanglement sum rule for $(d{-}1)$-dimensional quantum lattice models with finite abelian higher-form symmetries, obtained by minimally coupling a sector on $p$-simplices carrying a $p$-form $G$ symmetry to a sector on $(p{+}1)$-simplices carrying the dual $(d{-}p{-}2)$-form $\widehat G$ symmetry (with $\widehat G$ the Pontryagin dual of $G$). The coupling is introduced by conjugation with a symmetry-preserving operator $\mathcal{U}$ that dresses symmetry-invariant operators with appropriate Wilson operators. Our main result concerns symmetric eigenstates of the coupled model that arise by acting with $\mathcal{U}$ on direct-product, symmetric eigenstates of the decoupled model: provided a topological criterion formulated via the Mayer--Vietoris sequence holds for the chosen bipartition, $\mathcal{U}$ factorizes across the cut when acting on the symmetric state, and the bipartite entanglement entropy equals the sum of the entropies of the two sectors. The framework explains and generalizes known examples in fermion-$\mathbb{Z}_2$ gauge theory, identifies when topology obstructs the factorization, and provides a procedure to construct new examples by gauging higher-form symmetries.

Related papers

• Generalized cluster states in 2+1d: non-invertible symmetries, interfaces, and parameterized families [0.0]
  We construct 2+1-dimensional lattice models of symmetry-protected topological phases with non-invertible symmetries.<n>We study the symmetry acting on the interface between two generalized cluster states.<n>We also study the topological charge pumping phenomena, known as the generalized Thouless pump.
  arXiv  Detail & Related papers  (2026-01-13T15:00:00Z)
• Trading Mathematical for Physical Simplicity: Bialgebraic Structures in Matrix Product Operator Symmetries [20.76275069383104]
  We show that simple quantum spin chains of physical interest are not included in the rigid framework of fusion categories and weak Hopf algebras.<n>We show that our work provides a bridge between well-understood topological defect symmetries and those that arise in more realistic models.
  arXiv  Detail & Related papers  (2025-09-03T18:01:22Z)
• Detection of 2D SPT phases under decoherence [4.172680957016117]
  We propose a bulk order parameter for extracting symmetry-protected topological (SPT) invariants on a two dimensional lattice using partial symmetries.<n>We demonstrate this explicitly using a class of mixed states obtained from CZX-type models with $bbZtimesmathbbZ$ symmetry and $A$ symmetries.<n>We also comment on the practical detection of SPT invariants in quantum simulators through randomized measurements.
  arXiv  Detail & Related papers  (2025-06-30T18:00:03Z)
• $\mathbb{Z}_2$ gauging and self-dualities of the $XX$ model and its cousins [0.6073572808831218]
  We investigate the one-dimensional $XX$ lattice model and its cousins through the lens of momentum and winding $U(1)$ symmetries.<n>We distinguish two closely related $mathbbZ$ symmetries based on their relation to the $U(1)$ symmetries, and establish a web of $mathbbZulo$-gauging relations.
  arXiv  Detail & Related papers  (2025-03-03T18:55:01Z)
• Topological nature of edge states for one-dimensional systems without symmetry protection [46.87902365052209]
  We numerically verify and analytically prove a winding number invariant that correctly predicts the number of edge states in one-dimensional, nearest-neighbor (between unit cells)<n>Our winding number is invariant under unitary or similarity transforms.
  arXiv  Detail & Related papers  (2024-12-13T19:44:54Z)
• Multipartite entanglement in the diagonal symmetric subspace [39.58317527488534]
  For diagonal symmetric states, we show that there is no bound entanglement for $d = 3,4 $ and $N = 3$.<n>We present a constructive algorithm to map multipartite diagonal symmetric states of qudits onto bipartite symmetric states of larger local dimension.
  arXiv  Detail & Related papers  (2024-03-08T12:06:16Z)
• Symmetry-restricted quantum circuits are still well-behaved [45.89137831674385]
  We show that quantum circuits restricted by a symmetry inherit the properties of the whole special unitary group $SU(2n)$. It extends prior work on symmetric states to the operators and shows that the operator space follows the same structure as the state space.
  arXiv  Detail & Related papers  (2024-02-26T06:23:39Z)
• Quantum Current and Holographic Categorical Symmetry [62.07387569558919]
  A quantum current is defined as symmetric operators that can transport symmetry charges over an arbitrary long distance. The condition for quantum currents to be superconducting is also specified, which corresponds to condensation of anyons in one higher dimension.
  arXiv  Detail & Related papers  (2023-05-22T11:00:25Z)
• Deep Learning Symmetries and Their Lie Groups, Algebras, and Subalgebras from First Principles [55.41644538483948]
  We design a deep-learning algorithm for the discovery and identification of the continuous group of symmetries present in a labeled dataset. We use fully connected neural networks to model the transformations symmetry and the corresponding generators. Our study also opens the door for using a machine learning approach in the mathematical study of Lie groups and their properties.
  arXiv  Detail & Related papers  (2023-01-13T16:25:25Z)
• Towards Antisymmetric Neural Ansatz Separation [48.80300074254758]
  We study separations between two fundamental models of antisymmetric functions, that is, functions $f$ of the form $f(x_sigma(1), ldots, x_sigma(N)) These arise in the context of quantum chemistry, and are the basic modeling tool for wavefunctions of Fermionic systems.
  arXiv  Detail & Related papers  (2022-08-05T16:35:24Z)
• Conformal bridge transformation, $\mathcal{PT}$- and super- symmetry [0.0]
  Supersymmetric extensions of the 1D and 2D Swanson models are investigated by applying the conformal bridge transformation (CBT) to the first order Berry-Keating Hamiltonian multiplied by $i$ and its conformally neutral enlargements.
  arXiv  Detail & Related papers  (2021-12-26T22:05:33Z)

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.