Topological quantum phase transitions and criticality in a longer-range Kitaev chain

Abstract

In an attempt to theoretically investigate the quantum phase transition and criticality in topological models, we study a Kitaev chain with longer-range couplings (finite number of neighbors) as well as truly long-range couplings (infinite number of neighbors). We carry out an extensive topological 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 longer-rangeness in the system. We derive topological quantum critical lines and study them to understand the behavior of criticality. A suppression of higher order winding numbers is observed with decreasing longer-rangeness in the model. We show that the mechanism behind such phenomena is due to the superposition and vanishing of the topological quantum critical lines associated with the higher winding number. Through the study of the Berry connection, we show the possible different behaviors of critical lines when they undergo superposition along with the corresponding critical exponents. We analyze the behavior of the long-range models through the momentum space characterization. We also provide the exact solution for the problem and discuss the experimental aspects of the work.

Mixed state behavior of Hermitian and non-Hermitian topological models with extended couplings

“…The pseudo-spin (winding) vectors play an important role in defining the topology of a two level system. The number of time WVs rotate or wrap the center of parameter space gives the WN 42,81 . Here we consider the normalized WVs, which wrap the center of the maximally mixed states.…”

“…However, the question about measurement of higher WNs at finite temperature still remains unanswered. In a recent work, we have observed the staircase of topological transitions in 1D extended-range models 42 . The extended-range of coupling creates higher WNs, and the model reduces to short-range with the increase in the decay parameter.…”

“…Topological phases are characterized based on the numbers called topological invariants, which are in correspondence with the number of localized edge modes 40,41 . It is possible to generate higher winding numbers (WNs) either by increasing the number of coupling sites (static method) 42 or by periodic driving (dynamical method) 43 . However, this observation is true for BDI and AIII symmetry classes and holds good only for certain limit.…”

Topological phase transition between non-high symmetry critical phases and curvature function renormalization group

“…Therefore, using the good control over the nearest neighbors provided by these platforms one can study the results discussed in this work. As the non-HS criticality becomes prominent with increasing nearest-neighbor couplings 14,44,45 , an interesting question is whether the unique topological transition survive in truly long-range models. Moreover, the study of this interesting phenomena in non-Hermitian systems 58 , spin systems 45 and driven systems 20,59 sets the future direction of the work.…”

“…The topological invariant shows quantized jump associated with the bulk gap closing at a critical point. Therefore, a topological transition between distinct gapped phases is characterized by the bulk gap closing and opening along with the quantized jump in the values of invariant numbers [11][12][13][14] .…”