Motivated by recent developments in the field of 1D topological superconductors (TSCs), we investigate the phase transition properties of p-wave superconductor with 50 sites. In this paper, we first map the p-wave fermion model into the transverse [Formula: see text] model with an incommensurate modulated transverse field. We study the phase transition from TSC phase to Anderson localization phase by using imaginary time-evolving block decimation (TEBD) algorithm. By calculating the correlation function [Formula: see text], we numerically calculate the average correlation function in different p-wave pairing amplitude [Formula: see text]. By plotting the average correlation function versus the strength of incommensurate [Formula: see text] for [Formula: see text] and [Formula: see text], we identify the phase transition from TSC phase to Anderson localization phase [X. M. Cai et al., Phys. Rev. Lett. 110, 176403 (2013)]. Last but not least, we give an average measure of the entanglement of a single site with the rest of the system and von Neumann entropy of two boundary sites for the same parameters showing that the system possesses very strong entanglement at the critical point. The finite size effect and Majorana fermions are discussed in this paper.
Song and Mason Equation of State for Refrigerants
