Abstract
We study the spin transport through a 1D quantum Ising-XY-Ising spin link that emulates a topological superconducting-normal-superconducting structure via Jordan-Wigner (JW) transformation. We calculate, both analytically and numerically, the spectrum of spin Andreev bound states and the resulting $\mathbb{Z}_2$ fractional spin Josephson effect (JE) pertaining to the emerging Majorana JW fermions. Deep in the topological regime, we identify an effective time-reversal symmetry that leads to $\mathbb{Z}_4$ fractional spin JE in the $\textit{presence}$ of interactions within the junction. Moreover, we uncover a hidden inversion time-reversal symmetry that protects the $\mathbb{Z}_4$ periodicity in chains with an odd number of spins, even in the $\textit{absence}$ of interactions. We also analyze the entanglement between pairs of spins by evaluating the concurrence in the presence of spin current and highlight the effects of the JW Majorana states. We propose to use a microwave cavity setup for detecting the aforementioned JEs by dispersive readout methods and show that, surprisingly, the $\mathbb{Z}_2$ periodicity is immune to $\textit{any}$ local magnetic perturbations. Our results are relevant for a plethora of spin systems, such as trapped ions, photonic lattices, electron spins in quantum dots, or magnetic impurities on surfaces.
Highlights
Condensed-matter systems provide an endless playground for emergent exotic phenomena and quasiparticles
Deep in the topological regime, we identify an effective time-reversal symmetry that leads to Z4 fractional spin Josephson effect (JE) in the presence of interactions within the junction
In the case of |g| < 2t, the fermionic chain will be in a topological phase where Majorana fermions appear at the edges if we cut off the chain, and the corresponding topological invariant is characterized by the topological winding number W = 1
Summary
Condensed-matter systems provide an endless playground for emergent exotic phenomena and quasiparticles. We evaluate the entanglement between spins and show that it can be enhanced in the presence of a spin current owing to the misaligned Ising axes This effect, while present in the spin chain, does not have a fermionic counterpart in topological superconductors. Spin current is injected into the metal which is converted, via the SOI, into charge current and can be measured by usual means [46] While this method is effective for large spin systems, the signal might be too small for quantum spin chains.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
