# Observation of topological Euler insulators with a trapped-ion quantum simulator

@inproceedings{Zhao2022ObservationOT, title={Observation of topological Euler insulators with a trapped-ion quantum simulator}, author={W.-D. Zhao and Y-B Yang and Y. Jiang and Z.-C. Mao and W.-X. Guo and L-Y Qiu and G.-X. Wang and L. Yao and L. He and Z.-C. Zhou and Y. Xu and Luming Duan}, year={2022} }

Symmetries play a crucial role in the classiﬁcation of topological phases of matter. Although recent studies have established a powerful framework to search for and classify topological phases based on symmetry indicators, there exists a large class of fragile topology beyond the description. The Euler class characterizing the topology of two-dimensional real wave functions is an archetypal fragile topology underlying some important properties, such as non-Abelian braiding of crossing nodes and…

## 3 Citations

### Floquet multi-gap topology: Non-Abelian braiding and anomalous Dirac string phase

- Physics
- 2022

Topological phases of matter span a wide area of research shaping fundamental pursuits and oﬀering promise for future applications. While a signiﬁcant fraction of topological materials has been…

### Experimental observation of meronic topological acoustic Euler insulators

- Physics
- 2022

We report on the experimental observation of a gapped nontrivial Euler topology in an acoustic metamaterial. The topological invariant in this case is the Euler class, which characterizes the…

### Multi-gap topological conversion of Euler class via band-node braiding: minimal models, $PT$-linked nodal rings, and chiral heirs

- Physics
- 2022

The past few years have seen rapid progress in characterizing topological band structures using symmetry eigenvalue indicated methods. Recently, however, there has been increasing theoretical and…

## References

SHOWING 1-10 OF 62 REFERENCES

### Quantum Phases of Three-Dimensional Chiral Topological Insulators on a Spin Quantum Simulator.

- PhysicsPhysical review letters
- 2020

This work investigates the three-dimensional topological insulators in the AIII (chiral unitary) symmetry class, which yet lack experimental realization, and experimentally demonstrates their topological properties, where a dynamical quenching approach is adopted and the dynamical bulk-boundary correspondence in the momentum space is observed.

### Topological Euler Class as a Dynamical Observable in Optical Lattices.

- PhysicsPhysical review letters
- 2020

It is theoretically demonstrate that quenching with nontrivial Euler Hamiltonian results in stable monopole-antimonopole pairs, which in turn induce a linking of momentum-time trajectories under the first Hopf map, making the invariant experimentally observable.

### Observation of Topological Links Associated with Hopf Insulators in a Solid-State Quantum Simulator*

- Physics
- 2017

Hopf insulators are intriguing three-dimensional topological insulators characterized by an integer topological invariant. They originate from the mathematical theory of Hopf fibration and epitomize…

### Observation of symmetry-protected topological band with ultracold fermions

- PhysicsScience Advances
- 2018

This work reports the observation for ultracold atoms of a noninteracting SPT band in a one-dimensional optical lattice and studies quench dynamics between topologically distinct regimes, revealing two fundamental types of spin-relaxation dynamics related to bulk topology.

### Experimental observation of non-Abelian topological charges and edge states.

- MathematicsNature
- 2021

This work opens the door towards characterization and manipulation of non-Abelian topological charges, which may lead to interesting observables such as trajectory-dependent Dirac/Weyl node collisions in two-dimensional systems, admissible nodal line configurations in three dimensions, and may provide insight into certain strongly correlated phases of twisted bilayer graphene.

### Quantum Simulation for Three-Dimensional Chiral Topological Insulator.

- PhysicsPhysical review letters
- 2020

This work builds up a quantum simulator using nitrogen-vacancy center to investigate a three-dimensional (3D) chiral topological insulator, and demonstrates how a full study of topological phases can be achieved in quantum simulators.

### Classification of topological quantum matter with symmetries

- Physics
- 2016

Topological materials have become the focus of intense research in recent years, since they exhibit fundamentally new physical phenomena with potential applications for novel devices and quantum…

### Observation of a symmetry-protected topological phase of interacting bosons with Rydberg atoms

- PhysicsScience
- 2019

The experimental realization of a symmetry-protected topological phase of interacting bosons in a one-dimensional lattice is reported and a robust ground state degeneracy attributed to protected zero-energy edge states is demonstrated.

### Observation of Topological Magnon Insulator States in a Superconducting Circuit.

- PhysicsPhysical review letters
- 2019

This experiment experimentally realizes a tunable dimerized spin chain model and observes the topological magnon insulator states in a superconducting qubit chain and exhibits the great potential of tunable super Conducting Qubit chain as a versatile platform for exploring noninteracting and interacting symmetry-protected topological states.

### Scheme to Measure the Topological Number of a Chern Insulator from Quench Dynamics.

- Physics, MathematicsPhysical review letters
- 2017

It is shown how the topological number of astatic Hamiltonian can be measured from a dynamical quench process, and it is shown that the linking number of the trajectories of the phase vortices determines the phase boundary of the static Hamiltonian.