Gauging modulated symmetries: Kramers-Wannier dualities and non-invertible reflections
- URL: http://arxiv.org/abs/2406.12962v3
- Date: Fri, 17 Jan 2025 15:00:54 GMT
- Title: Gauging modulated symmetries: Kramers-Wannier dualities and non-invertible reflections
- Authors: Salvatore D. Pace, Guilherme Delfino, Ho Tat Lam, Ă–mer M. Aksoy,
- Abstract summary: Modulated symmetries are internal symmetries that act in a non-uniform, spatially modulated way.
In this paper, we systematically study the gauging of finite Abelian modulated symmetries in $1+1$ dimensions.
- Score: 0.0
- License:
- Abstract: Modulated symmetries are internal symmetries that act in a non-uniform, spatially modulated way and are generalizations of, for example, dipole symmetries. In this paper, we systematically study the gauging of finite Abelian modulated symmetries in ${1+1}$ dimensions. Working with local Hamiltonians of spin chains, we explore the dual symmetries after gauging and their potential new spatial modulations. We establish sufficient conditions for the existence of an isomorphism between the modulated symmetries and their dual, naturally implemented by lattice reflections. For instance, in systems of prime qudits, translation invariance guarantees this isomorphism. For non-prime qudits, we show using techniques from ring theory that this isomorphism can also exist, although it is not guaranteed by lattice translation symmetry alone. From this isomorphism, we identify new Kramers-Wannier dualities and construct related non-invertible reflection symmetry operators using sequential quantum circuits. Notably, this non-invertible reflection symmetry exists even when the system lacks ordinary reflection symmetry. Throughout the paper, we illustrate these results using various simple toy models.
Related papers
- A non-semisimple non-invertible symmetry [0.5932505549359508]
We investigate the action of a non-semisimple, non-invertible symmetry on spin chains.
We find a model where a product state and the so-called W state spontaneously break the symmetry.
arXiv Detail & Related papers (2024-12-27T13:27:24Z) - 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-neighbour (between unit cells)
Our invariant is invariant under unitary and similarity transforms.
arXiv Detail & Related papers (2024-12-13T19:44:54Z) - Variational Inference Failures Under Model Symmetries: Permutation Invariant Posteriors for Bayesian Neural Networks [43.88179780450706]
We investigate the impact of weight space permutation symmetries on variational inference.
We devise a symmetric symmetrization mechanism for constructing permutation invariant variational posteriors.
We show that the symmetrized distribution has a strictly better fit to the true posterior, and that it can be trained using the original ELBO objective.
arXiv Detail & Related papers (2024-08-10T09:06:34Z) - Non-invertible SPT, gauging and symmetry fractionalization [2.541410020898643]
We construct the lattice models for the phases of all the symmetries in the Rep($Q_8$) duality web.
We show that these interplay can be explained using the symmetry fractionalization in the 2+1d bulk SET.
arXiv Detail & Related papers (2024-05-24T21:35:55Z) - Non-invertible and higher-form symmetries in 2+1d lattice gauge theories [0.0]
We explore exact generalized symmetries in the standard 2+1d lattice $mathbbZ$ gauge theory coupled to the Ising model.
One model has a (non-anomalous) non-invertible symmetry, and we identify two distinct non-invertible symmetry protected topological phases.
We discuss how the symmetries and anomalies in these two models are related by gauging, which is a 2+1d version of the Kennedy-Tasaki transformation.
arXiv Detail & Related papers (2024-05-21T18:00:00Z) - 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) - Identifying the Group-Theoretic Structure of Machine-Learned Symmetries [41.56233403862961]
We propose methods for examining and identifying the group-theoretic structure of such machine-learned symmetries.
As an application to particle physics, we demonstrate the identification of the residual symmetries after the spontaneous breaking of non-Abelian gauge symmetries.
arXiv Detail & Related papers (2023-09-14T17:03:50Z) - Theory of Quantum Circuits with Abelian Symmetries [0.0]
Generic unitaries respecting a global symmetry cannot be realized, even approximately, using gates that respect the same symmetry.
We show that while the locality of interactions still imposes additional constraints on realizable unitaries, certain restrictions do not apply to circuits with Abelian symmetries.
This result suggests that global non-Abelian symmetries may affect the thermalization of quantum systems in ways not possible under Abelian symmetries.
arXiv Detail & Related papers (2023-02-24T05:47:13Z) - Symmetry protected entanglement in random mixed states [0.0]
We study the effect of symmetry on tripartite entanglement properties of typical states in symmetric sectors of Hilbert space.
In particular, we consider Abelian symmetries and derive an explicit expression for the logarithmic entanglement negativity of systems with $mathbbZ_N$ and $U(1)$ symmetry groups.
arXiv Detail & Related papers (2021-11-30T19:00:07Z) - Generalized string-nets for unitary fusion categories without
tetrahedral symmetry [77.34726150561087]
We present a general construction of the Levin-Wen model for arbitrary multiplicity-free unitary fusion categories.
We explicitly calculate the matrix elements of the Hamiltonian and, furthermore, show that it has the same properties as the original one.
arXiv Detail & Related papers (2020-04-15T12:21:28Z) - Inverse Learning of Symmetries [71.62109774068064]
We learn the symmetry transformation with a model consisting of two latent subspaces.
Our approach is based on the deep information bottleneck in combination with a continuous mutual information regulariser.
Our model outperforms state-of-the-art methods on artificial and molecular datasets.
arXiv Detail & Related papers (2020-02-07T13:48:52Z)
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.