Bulk topological signatures of a quasicrystal

Abstract

We show how measuring real space properties such as the charge density in a quasiperiodic system can be used to gain insight into their topological properties. In particular, for the Fibonacci chain, we show that the total onsite charge oscillates when plotted in the appropriate coordinates, and the number of oscillations is given by the Chern number of the gap in which the Fermi level lies. We show that these oscillations have two distinct interpretations, obtained by extrapolating results from the two extreme limits of the Fibonacci chain -- the valence bond picture in the strong modulation limit, and perturbation around the periodic chain in the weak modulation limit. This effect is found to remain robust at moderate interactions, as well as in the presence of disorder. We conclude that experimental measurement of the real space charge distribution can yield information on topological properties in a straightforward way.

arXiv comment8 pages, 6 figures

References in corpus (16)

• The density-matrix renormalization group in the age of matrix product states
• Entanglement Entropy and Quantum Field Theory
• Kwant: a software package for quantum transport
• Efficient numerical simulations with Tensor Networks: Tensor Network Python (TeNPy)
• Experimental realization and characterization of an electronic Lieb lattice
• Topological Equivalence between the Fibonacci Quasicrystal and the Harper Model
• Design and characterization of electronic fractals
• Topological Pumping over a Photonic Fibonacci Quasicrystal
• Fractal energy spectrum of a polariton gas in a Fibonacci quasi-periodic potential
• Measuring topological invariants from generalized edge states in polaritonic quasicrystals
• Revealing the topology of quasicrystals with a diffraction experiment
• Entanglement entropy of aperiodic quantum spin chains
• The Proximity Effect in a Superconductor-Quasicrystal Hybrid Ring
• Quasiperiodicity and 2D Topology in 1D Charge Ordered Materials
• Nonmonotonic crossover and scaling behaviors in a disordered 1D quasicrystal
• Detection of Topology via Entanglement Oscillations

Cited by in corpus (9)

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• Hyperuniform electron distributions controlled by electron interactions in quasicrystal
• Josephson effect in a Fibonacci quasicrystal
• Topological superconductivity in Fibonacci quasicrystals
• Closing of gaps and gap labeling and passage from molecular states to critical states in a 2D quasicrystal
• Edge and corner superconductivity in a 2D topological model
• Fibonacci-Modulation-Induced Multiple Topological Anderson Insulators
• Quantum state transfer and maximal entanglement between distant qubits using a minimal quasicrystal pump