Coexistence of magnetic and topological phases in spin-1/2 anisotropic extended XY chain
RK Malakar, AK Ghosh - arXiv preprint arXiv:2310.11243, 2023 - arxiv.org
arXiv preprint arXiv:2310.11243, 2023•arxiv.org
In this study, a spin-1/2 anisotropic extended XY chain has been introduced in which both
time reversal and SU (2) symmetries are broken but $ Z_2 $ symmetry is preserved. System
exhibits the faithful coexistence of magnetic and topological superconducting phases even
in the presence of transverse magnetic field. Location of those phases in the parameter
space has been determined precisely. Quantum phase transition is noted at zero magnetic
field, as well as magnetic long range order is found to withstand magnetic field of any …
time reversal and SU (2) symmetries are broken but $ Z_2 $ symmetry is preserved. System
exhibits the faithful coexistence of magnetic and topological superconducting phases even
in the presence of transverse magnetic field. Location of those phases in the parameter
space has been determined precisely. Quantum phase transition is noted at zero magnetic
field, as well as magnetic long range order is found to withstand magnetic field of any …
In this study, a spin-1/2 anisotropic extended XY chain has been introduced in which both time reversal and SU(2) symmetries are broken but symmetry is preserved. System exhibits the faithful coexistence of magnetic and topological superconducting phases even in the presence of transverse magnetic field. Location of those phases in the parameter space has been determined precisely. Quantum phase transition is noted at zero magnetic field, as well as magnetic long range order is found to withstand magnetic field of any strength. Exact analytic results for spin-spin correlation functions have been obtained in terms of Jordan Wigner fermionization. Existence of long range magnetic order has been investigated numerically by finding correlation functions as well as the Binder cumulant in the ground state. Dispersion relation, ground state energy, and energy gap are obtained analytically. In order to find the topologically nontrivial phase, sign of Pfaffian invariant and value of winding number have been evaluated. Both magnetic and topological phases are robust against the magnetic field and found to move coercively in the parameter space with the variation of its strength. Long range orders along two orthogonal directions and two different topological phases are found and their one-to-one correspondence has been established. Finally casting the spinless fermions onto Majorana fermions, properties of zero energy edge states are studied. Three different kinds of Majorana pairings are noted. In the trivial phase, next-nearest-neighbor Majorana pairing is found, whereas two different types of nearest-neighbor Majorana pairings are identified in the topological superconducting phase.
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