Majorana zero modes in a quantum Ising chain with longer-ranged interactions

Details Majorana zero modes in a quantum Ising chain with longer-ranged interactions Majorana zero modes in a quantum Ising chain with longer-ranged interactions

2011-10-13

arxiv.org/abs/1110.3072v2

Phys. Rev. B 85, 035110 (2012)

Physics

Condensed Matter

Strongly Correlated Electrons

11 pages, 8 figures; brief clarifying comments added; few new references; this version is accepted in Phys. Rev. B

Scientific paper

10.1103/PhysRevB.85.035110

A one-dimensional Ising model in a transverse field can be mapped onto a system of spinless fermions with p-wave superconductivity. In the weak-coupling BCS regime, it exhibits a zero energy Majorana mode at each end of the chain. Here, we consider a variation of the model, which represents a superconductor with longer ranged kinetic energy and pairing amplitudes, as is likely to occur in more realistic systems. It possesses a richer zero temperature phase diagram and has several quantum phase transitions. From an exact solution of the model these phases can be classified according to the number of Majorana zero modes of an open chain: 0, 1, or 2 at each end. The model posseses a multicritical point where phases with 0, 1, and 2 Majorana end modes meet. The number of Majorana modes at each end of the chain is identical to the topological winding number of the Anderson's pseudospin vector that describes the BCS Hamiltonian. The topological classification of the phases requires a unitary time-reversal symmetry to be present. When this symmetry is broken, only the number of Majorana end modes modulo 2 can be used to distinguish two phases. In one of the regimes, the wave functions of the two phase shifted Majorana zero modes decays exponentially in space but but in an oscillatory manner. The wavelength of oscillation is identical to the asymptotic connected spin-spin correlation of the XY-model in a transverse field to which our model is dual.

Affiliated with

Also associated with

No associations

Rating

Majorana zero modes in a quantum Ising chain with longer-ranged interactions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Majorana zero modes in a quantum Ising chain with longer-ranged interactions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Majorana zero modes in a quantum Ising chain with longer-ranged interactions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-521553