Exotic Symmetry Breaking Properties of Self-Dual Fracton Spin Models

• URL: http://arxiv.org/abs/2311.11066v2
• Date: Thu, 28 Mar 2024 17:02:51 GMT
• Title: Exotic Symmetry Breaking Properties of Self-Dual Fracton Spin Models
• Authors: Giovanni Canossa, Lode Pollet, Miguel A. Martin-Delgado, Hao Song, Ke Liu,
• Abstract summary: We investigate the ground-state properties and phase transitions of two self-dual fracton spin models. We show that both models experience a strong first-order phase transition with an anomalous $L-(D-1)$ scaling. Our work provides new understanding of sub-dimensional symmetry breaking and makes an important step for studying quantum-error-correction properties of the checkerboard and Haah's codes.
• Score: 4.467896011825295
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Fracton codes host unconventional topological states of matter and are promising for fault-tolerant quantum computation due to their large coding space and strong resilience against decoherence and noise. In this work, we investigate the ground-state properties and phase transitions of two prototypical self-dual fracton spin models -- the tetrahedral Ising model and the fractal Ising model -- which correspond to error-correction procedures for the representative fracton codes of type-I and type-II, the checkerboard code and the Haah's code, respectively, in the error-free limit. They are endowed with exotic symmetry-breaking properties that contrast sharply with the spontaneous breaking of global symmetries and deconfinement transition of gauge theories. To show these unconventional behaviors, which are associated with sub-dimensional symmetries, we construct and analyze the order parameters, correlators, and symmetry generators for both models. Notably, the tetrahedral Ising model acquires an extended semi-local ordering moment, while the fractal Ising model fits into a polynomial ring representation and leads to a fractal order parameter. Numerical studies combined with analytical tools show that both models experience a strong first-order phase transition with an anomalous $L^{-(D-1)}$ scaling, despite the fractal symmetry of the latter. Our work provides new understanding of sub-dimensional symmetry breaking and makes an important step for studying quantum-error-correction properties of the checkerboard and Haah's codes.

Related papers

• Non-invertible duality and symmetry topological order of one-dimensional lattice models with spatially modulated symmetry [0.0]
  We investigate interplay between self-duality and spatially modulated symmetry of $N$-state clock models. We find that the duality is non-invertible when the spatially modulated symmetry remains nontrivial. Our results illuminate a relationship between spatially modulated symmetry and ultraviolet/infrared mixing in one higher dimension.
  arXiv  Detail & Related papers  (2024-11-06T19:00:01Z)
• Entanglement and the density matrix renormalisation group in the generalised Landau paradigm [0.0]
  We leverage the interplay between gapped phases and dualities of symmetric one-dimensional quantum lattice models. For every phase in the phase diagram, the dual representation of the ground state that breaks all symmetries minimises both the entanglement entropy and the required number of variational parameters. Our work testifies to the usefulness of generalised non-invertible symmetries and their formal category theoretic description for the nuts and bolts simulation of strongly correlated systems.
  arXiv  Detail & Related papers  (2024-08-12T17:51:00Z)
• 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)
• 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)
• Oracle-Preserving Latent Flows [58.720142291102135]
  We develop a methodology for the simultaneous discovery of multiple nontrivial continuous symmetries across an entire labelled dataset. The symmetry transformations and the corresponding generators are modeled with fully connected neural networks trained with a specially constructed loss function. The two new elements in this work are the use of a reduced-dimensionality latent space and the generalization to transformations invariant with respect to high-dimensional oracles.
  arXiv  Detail & Related papers  (2023-02-02T00:13:32Z)
• Modeling the space-time correlation of pulsed twin beams [68.8204255655161]
  Entangled twin-beams generated by parametric down-conversion are among the favorite sources for imaging-oriented applications. We propose a semi-analytic model which aims to bridge the gap between time-consuming numerical simulations and the unrealistic plane-wave pump theory.
  arXiv  Detail & Related papers  (2023-01-18T11:29:49Z)
• Emergent XY* transition driven by symmetry fractionalization and anyon condensation [0.0]
  We study the phase diagram and anyon condensation transitions of a $mathbbZ$ topological order perturbed by Ising interactions in the Toric Code. The interplay between the global Ising symmetry and the lattice space group symmetries results in a non-trivial symmetry fractionalization class for the anyons. We provide numerical evidence for the occurrence of two symmetry breaking patterns predicted by the specific symmetry fractionalization class of the anyons in the explored phase diagram.
  arXiv  Detail & Related papers  (2022-04-07T18:00:00Z)
• Geometric phase in a dissipative Jaynes-Cummings model: theoretical explanation for resonance robustness [68.8204255655161]
  We compute the geometric phases acquired in both unitary and dissipative Jaynes-Cummings models. In the dissipative model, the non-unitary effects arise from the outflow of photons through the cavity walls. We show the geometric phase is robust, exhibiting a vanishing correction under a non-unitary evolution.
  arXiv  Detail & Related papers  (2021-10-27T15:27:54Z)
• 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)
• Many-Body Quantum States with Exact Conservation of Non-Abelian and Lattice Symmetries through Variational Monte Carlo [0.0]
  We present an ansatz where global non-abelian symmetries are inherently embedded in its structure. We extend the model to incorporate lattice symmetries as well.
  arXiv  Detail & Related papers  (2021-04-30T09:52:15Z)
• Tensor network models of AdS/qCFT [69.6561021616688]
  We introduce the notion of a quasiperiodic conformal field theory (qCFT) We show that qCFT can be best understood as belonging to a paradigm of discrete holography.
  arXiv  Detail & Related papers  (2020-04-08T18:00:05Z)

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.