Comparison of the proposed results with the state of the art numerical and analytical solutions reveals that the worth of our scheme in terms of accuracy and convergence. The design scheme is applied to solve TFE for five different scenarios by taking various step sizes and different input intervals. Optimization of parameters for the system is carried out with GAs, used as a tool for viable global search integrated with SQP algorithm for rapid refinement of the results. A fitness function is constructed based on the residual error of constituent equations in the mean square sense and is formulated as the minimization problem. The FDS procedures are used to transform the TFE differential equations into a system of nonlinear equations. 66, 129вЂ“192 (1994).In this study, a novel bio-inspired computing approach is developed to analyze the dynamics of nonlinear singular ThomasвЂ“Fermi equation (TFE) arising in potential and charge density models of an atom by exploiting the strength of finite difference scheme (FDS) for discretization and optimization through genetic algorithms (GAs) hybrid with sequential quadratic programming. Renormalization-group approach to interacting fermions. ElectronвЂ“electron interactions in graphene: Current status and perspectives. Polarization charge distribution in gapped graphene: Perturbation theory and exact diagonalization analysis. Gapless state of bismuth-type semimetals. Quantum critical point in graphene approached in the limit of infinitely strong Coulomb interaction. Signatures of a pressure-induced topological quantum phase transition in BiTeI. Emergence of non-centrosymmetric topological insulating phase in BiTeI under pressure.

Phase transition between the quantum spin Hall and insulator phases in 3D: Emergence of a topological gapless phase. Universal phase diagrams for the quantum spin Hall systems. Theory of topological quantum phase transitions in 3D noncentrosymmetric systems. Non-Fermi-liquid and topological states with strong spinвЂ“orbit coupling. SU(2) non-Abelian holonomy andВ dissipationless spin current in semiconductors. Quantum theory of cyclotron resonance in semiconductors: General theory. Quantum criticality between topological and band insulators in 3 + 1 dimensions. Renormalization group study of electromagnetic interaction in multi-Dirac-node systems. Theory of a quantum critical phenomenon in a topological insulator: (3 + 1)-dimensional quantum electrodynamics in solids. Weyl semimetal in a topological insulator multilayer. Variation of charge dynamics in the course of metalвЂ“insulator transition for pyrochlore type Nd2Ir2O7. Topological semimetal and Fermi-arc surface states in the electronic structure of pyrochlore iridates. Topological order: From long-range entangled quantum matter to a unified origin of light and electrons. Quantum Phase Transitions 2nd edn (Cambridge Univ.

The interplay between the anisotropic dispersion and the Coulomb interaction brings about a screening phenomenon distinct from the conventional ThomasвЂ“Fermi screening in metals and logarithmic screening in Dirac fermions. At the quantum critical point, the emerging low-energy fermions, dubbed the anisotropic Weyl fermions, show both relativistic and Newtonian dynamics simultaneously. Here we discover a class of quantum critical phenomena in topological materials for which either the inversion symmetry or time-reversal symmetry can be broken.

In conventional topological insulators in three dimensions, the low-energy theory near the gap-closing point can be described by relativistic Dirac fermions coupled to the long-range Coulomb interaction hence, the quantum critical point of topological phase transitions provides a promising platform to test the intriguing predictions of quantum electrodynamics. Topological phase transitions in condensed matter systems accompany emerging singularities of the electronic wavefunction, often manifested by gap-closing points in momentum space.

Thomas fermi screening parameter