Local order parameters for symmetry fractionalization

@article{GarreRubio2019LocalOP,
  title={Local order parameters for symmetry fractionalization},
  author={Jos{\'e} Garre-Rubio and Sofyan Iblisdir},
  journal={New Journal of Physics},
  year={2019}
}
We propose a family of order parameters to detect the symmetry fractionalization class of anyons in 2D topological phases. This fractionalization class accounts for the projective, as opposed to linear, representations of the symmetry group on the anyons. We focus on quantum double models on a lattice enriched with an internal symmetry in the framework of $G$-isometric projected entangled pair states. Unlike previous schemes based on reductions to effective 1D systems (dimensional… 

Figures and Tables from this paper

String order parameters for symmetry fractionalization in an enriched toric code
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
Subsystem symmetry enriched topological order in three dimensions
We introduce a model of three-dimensional (3D) topological order enriched by planar subsystem symmetries. The model is constructed starting from the 3D toric code, whose ground state can be viewed as
Non-Abelian hybrid fracton orders
We introduce lattice gauge theories which describe three-dimensional, gapped quantum phases exhibiting the phenomenology of both conventional three-dimensional topological orders and fracton orders,
Symmetries in topological tensor network states: classification, construction and detection
TLDR
This thesis contributes to the understanding of symmetry-enriched topological phases focusing on their descriptions in terms of tensor network states by proposing a family of gauge invariant quantities and their corresponding order parameters to detect the corresponding quantum phases, in particular their symmetry fractionalization patterns.
Many-body topological invariants from randomized measurements in synthetic quantum matter
TLDR
A universal toolbox of measurement protocols is proposed to reveal many-body topological invariants of phases with global symmetries, which can be implemented in state-of-the-art experiments with synthetic quantum systems, such as Rydberg atoms, trapped ions, and superconducting circuits.
Many-Body Chern Number from Statistical Correlations of Randomized Measurements.
TLDR
This work uses the statistical correlations of randomized measurements to infer the many-body Chern number of a wave function, and its results apply to disklike geometries that are more amenable to current quantum simulator architectures.
Matrix product states and projected entangled pair states: Concepts, symmetries, theorems
The theory of entanglement provides a fundamentally new language for describing interactions and correlations in many body systems. Its vocabulary consists of qubits and entangled pairs, and the

References

SHOWING 1-10 OF 80 REFERENCES
Symmetry fractionalization and twist defects
Topological order in two dimensions can be described in terms of deconfined quasiparticle excitations - anyons - and their braiding statistics. However, it has recently been realized that this data
Numerical detection of symmetry-enriched topological phases with space-group symmetry
Topologically ordered phases of matter, in particular so-called symmetry-enriched topological phases, can exhibit quantum number fractionalization in the presence of global symmetry. In Z_2
Measuring space-group symmetry fractionalization in Z 2 spin liquids
The interplay of symmetry and topological order leads to a variety of distinct phases of matter, the Symmetry Enriched Topological (SET) phases. Here we discuss physical observables that distinguish
Detection of symmetry-enriched topological phases
Topologically ordered systems in the presence of symmetries can exhibit new structures which are referred to as symmetry enriched topological (SET) phases. We introduce simple methods to detect the
Detection of symmetry-protected topological phases in one dimension
A topological phase is a phase of matter which cannot be characterized by a local order parameter. It has been shown that gapped symmetric phases in one-dimensional (1D) systems can be completely
Symmetry fractionalization in the topological phase of the spin-1/2 J(1)-J(2) triangular Heisenberg model
Using density-matrix renormalization-group calculations for infinite cylinders, we elucidate the properties of the spin-liquid phase of the spin-1/2 J(1)-J(2) Heisenberg model on the triangular
Symmetry protected topological orders and the group cohomology of their symmetry group
Symmetry protected topological (SPT) phases are gapped short-range-entangled quantum phases with a symmetry G. They can all be smoothly connected to the same trivial product state if we break the
Classification of gapped symmetric phases in one-dimensional spin systems
Quantum many-body systems divide into a variety of phases with very different physical properties. The questions of what kinds of phases exist and how to identify them seem hard, especially for
Order parameter for symmetry-protected phases in one dimension.
TLDR
An order parameter for symmetry-protected phases in one dimension which allows us to directly identify those phases and it is found that the order parameter not only works very well for the dimerized and the Haldane phase, but it also returns a distinct signature for gapless phases.
...
...