Evaluation of real-space second Chern number using the kernel polynomial method

Abstract

We evaluate the real-space second Chern number of four-dimensional Chern insulators using the kernel polynomial method. Our calculations are performed on a four-dimensional system with $30^4$ sites, and the numerical results agree well with theoretical expectations. Moreover, we show that the method is capable of capturing the disorder effects. This is evidenced by the phase diagram obtained for disordered systems, which agrees well with predictions from the self-consistent Born approximation. Furthermore, we extend the method to six dimensions and perform an exploratory real-space calculation of the third Chern number. Although finite-size effects prevent full quantization, the numerical results show qualitative agreement with theoretical expectations. The study represents a step forward in the real-space characterization of higher-dimensional topological phases.

References in corpus (43)

• Topological Insulators
• Topological insulators and superconductors
• Anyons in an exactly solved model and beyond
• Topological Field Theory of Time-Reversal Invariant Insulators
• The Kernel Polynomial Method
• Topological Anderson Insulator
• Photonic topological pumping through the edges of a dynamical four-dimensional quantum Hall system
• Theory of the topological Anderson insulator
• Three-dimensional quantum Hall effect and metal-insulator transition in ZrTe5
• Mapping topological order in coordinate space
• Entanglement Spectrum of a Disordered Topological Chern Insulator
• Four-Dimensional Quantum Hall Effect with Ultracold Atoms
• Disordered Topological Insulators via $C^{\ast }$-Algebras
• Quantum Hall effect in a bulk antiferromagnet EuMnBi${}_2$ with magnetically confined two-dimensional Dirac fermions
• Topological Photonic Quasicrystals: Fractal Topological Spectrum and Protected Transport
• 3D quantum Hall effect of Fermi arcs in topological semimetals
• Circuit Implementation of a Four-Dimensional Topological Insulator
• Observation of a non-Abelian Yang Monopole: From New Chern Numbers to a Topological Transition
• Real-space calculation of the conductivity tensor for disordered topological matter
• Statistical Topological Insulators
• 4D spinless topological insulator in a periodic electric circuit
• Theory of the Three Dimensional Quantum Hall Effect in Graphite
• The 6D quantum Hall effect and 3D topological pumps
• Theory for the Charge-Density-Wave Mechanism of 3D Quantum Hall Effect
• Four-Dimensional Higher-Order Chern Insulator and Its Acoustic Realization
• 3D Quantum Hall Effect Manipulated by Chiral Landau Levels in Weyl Semimetals
• Field-Tunable One-Sided Higher-Order Topological Hinge States in Dirac Semimetals
• Approaching Three-Dimensional Quantum Hall effect in Bulk HfTe5
• Computation of topological phase diagram of disordered Pb${}_{1-x}$Sn${}_x$Te using the kernel polynomial method
• Electric circuit simulations of $n$th-Chern insulators in $2n$-dimensional space and their non-Hermitian generalizations for arbitral $n$
• Universal topological marker
• The non-commutative n-th Chern number
• Local Topological Markers in Odd Spatial Dimensions and Their Application to Amorphous Topological Matter
• Three-Dimensional Quantum Anomalous Hall Effect in Ferromagnetic Insulators
• Local Topological Markers in Odd Dimensions
• Observation of higher-order topological states on a quantum computer
• Efficient algorithm to compute the second Chern number in four dimensional systems
• Revealing Chern number from quantum metric
• Robustness of topological order against disorder
• Phase transitions and scale invariance in topological Anderson insulators
• Scaling of the Integrated Quantum Metric in Disordered Topological Phases
• Topological gap labeling with the third Chern numbers in three-dimensional quasicrystals
• Real-space representation of the second Chern number

Cited by in corpus (2)

• Regularized universal topological markers for Dirac systems
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