Finite temperature topological states in a chain of magnetic adatoms on a superconductor

It is known that magnetic moments of a one-dimensional chain of adatoms on a superconductor self-organize into a spiral magnetic structure, which leads to topologically nontrivial superconductivity. Such a system can host the Majorana quasiparticles near its edges. The interaction between the localized moments is mediated by itinerant electrons. Upon tracing out the fermionic degrees of freedom, one obtains long range temperature-dependent effective interaction between the moments. Using Monte Carlo techniques we calculate the thermodynamic properties of the system. In particular, we demonstrate that with increasing temperature the correlation length of the magnetic order decreases, eventually driving the system to a topologically trivial phase. Using the simulated annealing method we also show, that at low temperature a phase separation can take place in the chain, where only part of the system is in the topologically nontrivial state and the rest of it is in the trivial state.