LAUSR

In an attempt to theoretically investigate the topological quantum phase transition and criticality in long-range models, we study an extended Kitaev chain. We carry out an extensive characterization of the momentum space to explore the possibility of obtaining higher order winding numbers and analyze the nature of their stability in the model. The occurrences of phase transitions from even-to-even and odd-to-odd winding numbers are observed with decreasing long-rangeness in the system. We derive topological quantum critical lines and study the universality class of critical exponents to understand the behavior of criticality. A suppression of higher order winding numbers is observed with decreasing long-rangeness in the model. We show that the mechanism behind such phenomena is due to the superposition and vanishing of the critical lines associated with the higher winding number. We also provide exact solution for the problem and discuss the experimental aspects of the work.