scholarly journals Real-space representation of the winding number for a one-dimensional chiral-symmetric topological insulator

2021 ◽  
Vol 103 (22) ◽  
Author(s):  
Ling Lin ◽  
Yongguan Ke ◽  
Chaohong Lee
Keyword(s):  
Topological Insulator ◽  
Real Space ◽  
Space Representation ◽  
Winding Number ◽  
One Dimensional

scholarly journals Vortex states in an acoustic Weyl crystal with a topological lattice defect

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Qiang Wang ◽  
Yong Ge ◽  
Hong-xiang Sun ◽  
Haoran Xue ◽  
Ding Jia ◽  
...  
Keyword(s):  
Angular Momentum ◽  
Orbital Angular Momentum ◽  
Lattice Defect ◽  
Three Dimensional ◽  
Surface States ◽  
Real Space ◽  
Lattice Defects ◽  
One Dimensional ◽  
Topological Features ◽  
Topological Lattice

AbstractCrystalline materials can host topological lattice defects that are robust against local deformations, and such defects can interact in interesting ways with the topological features of the underlying band structure. We design and implement a three dimensional acoustic Weyl metamaterial hosting robust modes bound to a one-dimensional topological lattice defect. The modes are related to topological features of the bulk bands, and carry nonzero orbital angular momentum locked to the direction of propagation. They span a range of axial wavenumbers defined by the projections of two bulk Weyl points to a one-dimensional subspace, in a manner analogous to the formation of Fermi arc surface states. We use acoustic experiments to probe their dispersion relation, orbital angular momentum locked waveguiding, and ability to emit acoustic vortices into free space. These results point to new possibilities for creating and exploiting topological modes in three-dimensional structures through the interplay between band topology in momentum space and topological lattice defects in real space.

scholarly journals Understanding Topological Insulators in Real Space

Molecules ◽  
2021 ◽  
Vol 26 (10) ◽  
pp. 2965
Author(s):  
Angel Martín Pendás ◽  
Francisco Muñoz ◽  
Carlos Cardenas ◽  
Julia Contreras-García
Keyword(s):  
Quantum Theory ◽  
Chiral Symmetry ◽  
Topological Insulator ◽  
Real Space ◽  
Electron Delocalization ◽  
Electron Localization ◽  
Visualization Tool ◽  
Atom Pairs ◽  
Chemical Concepts ◽  
Bulk Behavior

A real space understanding of the Su–Schrieffer–Heeger model of polyacetylene is introduced thanks to delocalization indices defined within the quantum theory of atoms in molecules. This approach enables to go beyond the analysis of electron localization usually enabled by topological insulator indices—such as IPR—enabling to differentiate between trivial and topological insulator phases. The approach is based on analyzing the electron delocalization between second neighbors, thus highlighting the relevance of the sublattices induced by chiral symmetry. Moreover, the second neighbor delocalization index, δi,i+2, also enables to identify the presence of chirality and when it is broken by doping or by eliminating atom pairs (as in the case of odd number of atoms chains). Hints to identify bulk behavior thanks to δ1,3 are also provided. Overall, we present a very simple, orbital invariant visualization tool that should help the analysis of chirality (independently of the crystallinity of the system) as well as spreading the concepts of topological behavior thanks to its relationship with well-known chemical concepts.

Resonances and Torsion Numbers of Driven Dissipative Nonlinear Oscillators

1986 ◽  
Vol 41 (4) ◽  
pp. 605-614 ◽  
Author(s):  
Ulrich Parlitz ◽  
Werner Lauterborn
Keyword(s):  
Nonlinear Oscillators ◽  
Winding Number ◽  
Local Flow ◽  
One Dimensional ◽  
Bifurcation Set ◽  
Local Bifurcations ◽  
Closed Orbits

The torsion of the local flow around closed orbits and its relation to the superstructure in the bifurcation set of strictly dissipative nonlinear oscillators is investigated. The torsion number describing the twisting behaviour of the flow turns out to be a suitable invariant for the classification of local bifurcations and resonances in those systems. Furthermore, the notions of winding number and resonance are generalized to arbitrary one-dimensional dissipative oscillators.

One-Dimensional Harmonic Oscillator in Quantum Phase Space

2011 ◽  
Vol 110-116 ◽  
pp. 3750-3754
Author(s):  
Jun Lu ◽  
Xue Mei Wang ◽  
Ping Wu
Keyword(s):  
Phase Space ◽  
Harmonic Oscillator ◽  
Quantum Phase ◽  
Space Representation ◽  
Wave Mechanics ◽  
One Dimensional ◽  
Matrix Mechanics ◽  
The Matrix ◽  
Quantum Wave ◽  
The One

Within the framework of the quantum phase space representation established by Torres-Vega and Frederick, we solve the rigorous solutions of the stationary Schrödinger equations for the one-dimensional harmonic oscillator by means of the quantum wave-mechanics method. The result shows that the wave mechanics and the matrix mechanics are equivalent in phase space, just as in position or momentum space.

scholarly journals Time-resolved observation of spin-charge deconfinement in fermionic Hubbard chains

Science ◽  
2020 ◽  
Vol 367 (6474) ◽  
pp. 186-189 ◽  
Author(s):  
Jayadev Vijayan ◽  
Pimonpan Sompet ◽  
Guillaume Salomon ◽  
Joannis Koepsell ◽  
Sarah Hirthe ◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Spatial Separation ◽  
Real Space ◽  
Quantum Gas ◽  
Interacting Particles ◽  
Time Resolved ◽  
One Dimensional ◽  
Quantum Numbers ◽  
Charge Correlations ◽  
The Individual

Elementary particles carry several quantum numbers, such as charge and spin. However, in an ensemble of strongly interacting particles, the emerging degrees of freedom can fundamentally differ from those of the individual constituents. For example, one-dimensional systems are described by independent quasiparticles carrying either spin (spinon) or charge (holon). Here, we report on the dynamical deconfinement of spin and charge excitations in real space after the removal of a particle in Fermi-Hubbard chains of ultracold atoms. Using space- and time-resolved quantum gas microscopy, we tracked the evolution of the excitations through their signatures in spin and charge correlations. By evaluating multipoint correlators, we quantified the spatial separation of the excitations in the context of fractionalization into single spinons and holons at finite temperatures.

Quantum entanglement in some topological insulator models

2019 ◽  
Vol 33 (24) ◽  
pp. 1950284 ◽  
Author(s):  
L. S. Lima
Keyword(s):  
Quantum Entanglement ◽  
Topological Insulator ◽  
Topological Charge ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Model Case ◽  
Topological Transition ◽  
One Dimensional ◽  
Zhang Model ◽  
The One

Quantum entanglement is studied in the neighborhood of a topological transition in some topological insulator models such as the two-dimensional Qi–Wu–Zhang model or Chern insulator. The system describes electrons hopping in two-dimensional chains. For the one-dimensional model case, there exist staggered hopping amplitudes. Our results show a strong effect of sudden variation of the topological charge Q in the neighborhood of phase transition on quantum entanglement for all the cases analyzed.

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