String order parameters for symmetry fractionalization in an enriched
toric code
- URL: http://arxiv.org/abs/2011.02981v2
- Date: Thu, 4 Mar 2021 10:48:35 GMT
- Title: String order parameters for symmetry fractionalization in an enriched
toric code
- Authors: Jos\'e Garre-Rubio, Mohsin Iqbal and David T. Stephen
- Abstract summary: We study a simple model of symmetry-enriched topological order obtained by decorating a toric code model with lower-dimensional symmetry-protected topological states.
We show that the symmetry fractionalization in this model can be characterized by string order parameters, and that these signatures are robust under the effects of external fields and interactions.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We study a simple model of symmetry-enriched topological order obtained by
decorating a toric code model with lower-dimensional symmetry-protected
topological states. We show that the symmetry fractionalization in this model
can be characterized by string order parameters, and that these signatures are
robust under the effects of external fields and interactions, up to the phase
transition point. This extends the recent proposal of [New Journal of Physics
21, 113016 (2019)] beyond the setting of fixed-point tensor network states, and
solidifies string order parameters as a useful tool to characterize and detect
symmetry fractionalization. In addition to this, we observe how the
condensation of an anyon that fractionalizes a symmetry forces that symmetry to
spontaneously break, and we give a proof of this in the framework of projected
entangled pair states. This phenomenon leads to a notable change in the phase
diagram of the toric code in parallel magnetic fields.
Related papers
- A Generative Model of Symmetry Transformations [44.87295754993983]
We build a generative model that explicitly aims to capture the data's approximate symmetries.
We empirically demonstrate its ability to capture symmetries under affine and color transformations.
arXiv Detail & Related papers (2024-03-04T11:32:18Z) - Engineering Hierarchical Symmetries [0.0]
We present a general driving protocol for many-body systems to generate a sequence of prethermal regimes.
We provide an explicit construction of effective Hamiltonians exhibiting these symmetries.
arXiv Detail & Related papers (2024-02-21T04:09:23Z) - Exotic Symmetry Breaking Properties of Self-Dual Fracton Spin Models [4.467896011825295]
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.
arXiv Detail & Related papers (2023-11-18T13:12:14Z) - 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) - 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) - Entanglement-enabled symmetry-breaking orders [0.0]
A spontaneous symmetry-breaking order is conventionally described by a tensor-product wave-function of some few-body clusters.
We discuss a type of symmetry-breaking orders, dubbed entanglement-enabled symmetry-breaking orders, which cannot be realized by any tensor-product state.
arXiv Detail & Related papers (2022-07-18T18:00:00Z) - 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) - Reflection and Rotation Symmetry Detection via Equivariant Learning [40.61825212385055]
We introduce a group-equivariant convolutional network for symmetry detection, dubbed EquiSym.
We present a new dataset, DENse and DIverse symmetry (DENDI), which mitigates limitations of existing benchmarks for reflection and rotation symmetry detection.
Experiments show that our method achieves the state of the arts in symmetry detection on LDRS and DENDI datasets.
arXiv Detail & Related papers (2022-03-31T04:18:33Z) - Classifying phases protected by matrix product operator symmetries using
matrix product states [0.0]
We classify the different ways in which matrix product states (MPSs) can stay invariant under the action of matrix product operator (MPO) symmetries.
This is achieved through a local characterization of how the MPSs, that generate a ground space, remain invariant under a global MPO symmetry.
arXiv Detail & Related papers (2022-03-23T17:25:30Z) - 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) - Symmetry Breaking in Symmetric Tensor Decomposition [44.181747424363245]
We consider the nonsymmetry problem associated with computing the points rank decomposition of symmetric tensors.
We show that critical points the loss function is detected by standard methods.
arXiv Detail & Related papers (2021-03-10T18:11:22Z)
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.