Breaking global symmetries with locality-preserving operations

• URL: http://arxiv.org/abs/2508.15892v1
• Date: Thu, 21 Aug 2025 18:00:02 GMT
• Title: Breaking global symmetries with locality-preserving operations
• Authors: Michele Mazzoni, Luca Capizzi, Lorenzo Piroli,
• Abstract summary: We show that locality-preserving operations can generate maximal asymmetry.<n>Our results highlight a non-trivial interplay between asymmetry, locality, and entanglement.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In the general framework of quantum resource theories, one typically only distinguishes between operations that can or cannot generate the resource of interest. In many-body settings, one can further characterize quantum operations based on underlying geometrical constraints, and a natural question is to understand the power of resource-generating operations that preserve locality. In this work, we address this question within the resource theory of asymmetry, which has recently found applications in the study of many-body symmetry-breaking and symmetry-restoration phenomena. We consider symmetries corresponding to both abelian and non-abelian compact groups with a homogeneous action on the space of $N$ qubits, focusing on the prototypical examples of $U(1)$ and $SU(2)$. We study the so-called $G$-asymmetry $\Delta S^{G}_N$, and present two main results. First, we derive a general bound on the asymmetry that can be generated by locality-preserving operations acting on product states. We prove that, in any spatial dimension, $\Delta S^{G}_N\leq (1/2)\Delta S^{G, \rm max}_N[1+o(1)]$, where $\Delta S^{G, \rm max}_N$ is the maximum value of the $G$-asymmetry in the full many-body Hilbert space. Second, we show that locality-preserving operations can generate maximal asymmetry, $\Delta S^{G}_N\sim\Delta S^{G, \rm max}_N$, when applied to symmetric states featuring long-range entanglement. Our results provide a unified perspective on recent studies of asymmetry in many-body physics, highlighting a non-trivial interplay between asymmetry, locality, and entanglement.

Related papers

• Entanglement Sum Rule from Higher-Form Symmetries [0.0]
  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.
  arXiv  Detail & Related papers  (2025-10-20T09:03:12Z)
• Entanglement Asymmetry and Quantum Mpemba Effect for Non-Abelian Global Symmetry [0.0]
  Entanglement asymmetry is a measure that quantifies the degree of symmetry breaking at the level of a subsystem.<n>We discuss the quantum Mpemba effect for SU$(N)$ symmetry, the phenomenon that the more symmetry is initially broken, the faster it is restored.
  arXiv  Detail & Related papers  (2025-09-06T05:01:12Z)
• Symmetry enforced entanglement in maximally mixed states [3.5602863178766966]
  Entanglement in quantum many-body systems is typically fragile to interactions with the environment.<n>We analyze the entanglement and correlations of the maximally mixed state in the invariant sector.<n>For all Abelian symmetries, the MMIS is separable, and for all non-Abelian symmetries, the MMIS is entangled.
  arXiv  Detail & Related papers  (2024-06-12T18:00:00Z)
• 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)
• Remarks on effects of projective phase on eigenstate thermalization hypothesis [0.0]
  We consider $mathbbZ_NtimesmathbbZ_N$ symmetries with nontrivial projective phases. We also perform numerical analyses for $ (1+1)$-dimensional spin chains and the $ (2+1)$-dimensional lattice gauge theory.
  arXiv  Detail & Related papers  (2023-10-17T17:36:37Z)
• How Over-Parameterization Slows Down Gradient Descent in Matrix Sensing: The Curses of Symmetry and Initialization [46.55524654398093]
  We show how over- parameterization changes the convergence behaviors of descent. The goal is to recover an unknown low-rank ground-rank ground-truth matrix from near-isotropic linear measurements. We propose a novel method that only modifies one step of GD and obtains a convergence rate independent of $alpha$.
  arXiv  Detail & Related papers  (2023-10-03T03:34:22Z)
• 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)
• Symmetry-enriched topological order from partially gauging symmetry-protected topologically ordered states assisted by measurements [1.2809525640002364]
  It is known that for a given symmetry group $G$, the 2D SPT phase protected by $G$ is dual to the 2D topological phase exemplified by the twisted quantum double model $Domega(G)$ via gauging the global symmetry $G$. Here, we review the general approach to gauging a $G$-SPT starting from a fixed-point ground-state wave function and applying a $N$-step gauging procedure. We provide an in-depth analysis of the intermediate states emerging during the N-step gauging and provide tools to measure and identify the emerging symmetry-
  arXiv  Detail & Related papers  (2023-05-16T18:40:56Z)
• 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)
• Fermion and meson mass generation in non-Hermitian Nambu--Jona-Lasinio models [77.34726150561087]
  We investigate the effects of non-Hermiticity on interacting fermionic systems. We do this by including non-Hermitian bilinear terms into the 3+1 dimensional Nambu--Jona-Lasinio (NJL) model.
  arXiv  Detail & Related papers  (2021-02-02T13:56:11Z)
• The Geometry of Time in Topological Quantum Gravity of the Ricci Flow [41.94295877935867]
  We continue the study of nonrelativistic quantum gravity associated with a family of Ricci flow equations.<n>This topological gravity is of the cohomological type, and it exhibits an $cal N=2$ extended BRST symmetry.<n>We demonstrate a standard one-step BRST gauge-fixing of a theory whose fields are $g_ij$, $ni$ and $n$, and whose gauge symmetries consist of (i) the topological deformations of $g_ij$, and (ii) the ultralocal nonrelativistic limit of space
  arXiv  Detail & Related papers  (2020-11-12T06:57:10Z)

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.