Detecting topological phase transition in 1D superconducting systems with next nearest neighbor hopping

Abstract

We investigate the effect of next-nearest-neighbor hopping on topological quantum phase transitions (QPTs) that are characterized by the number of Majorana zero modes in onedimensional (1D) p-wave superconducting systems. We also numerically analyze the scaling behavior and the universality of the Berry phase (BP) of the ground state close to the critical point. For critical line (I), the derivative of the ground-state BP is nonanalytic at the phase boundaries. For the phase boundary (II), a noncontractible BP of the ground state itself is also a witness of quantum phase transition.

Geometry of quantum phase transitions

“…The idea that QPTs could be explored through the Berry phase properties was first proposed and applied in the prototypical XY spin-1/2 chain [31,32,37,39,40,57,65,76] and extended to many other many-body systems, such as the Dicke model [38,44], the Lipkin-Meshkov-Glick model [43,60,72], Yang-Baxter spin-1/2 model [49,58], quasi free-Fermion systems [47,53,56,85,102], interacting Fermion models [51,63,68,77,79,98,116], in ultracold atoms [73,74,91], in spin chains with long range interactions [70,81], in cluster models [106], in the spin-boson model [114], in the 1D compassmodel [59,96], and in connection to spin-crossover phenomena [55]. The critical properties of the geometric phase has also been studied in few-body systems interacting with critical chains [66,67,78,87,92,97,100], in non-Hermitian critical systems [...…”