Many-body wave function and edge magnetization of an open $p+is$ superconducting chain

TL;DR

This paper derives an exact many-body wave function for a one-dimensional open $p+is$ superconductor, enabling explicit calculation of edge magnetization and providing insights into the system's quantum state.

Contribution

It constructs the first exact BCS ground state wave function for an open boundary $p+is$ superconductor, including approximate forms for small $s$-wave components.

Findings

Explicit edge magnetization calculations from the wave function

Approximate wave function form for small $s$-wave component

Deeper understanding of open $p+is$ superconducting chains

Abstract

Although BCS wave function for superconductors under periodic boundary conditions are well-established, obtaining an explicit form of the many-body BCS wave function under open boundary condition is usually a nontrivial problem. In this work, we construct the exact BCS ground state wave function of a one-dimensional spin-1/2 superconductor with $p+ is$ pairing symmetry under open boundary conditions for special sets of parameters. The spin magnetization on the edges are calculated explicitly using the obtained wave function. Approximate expression of the wave function is also discussed based on degenerate perturbation theory when the $s$-wave component is much smaller than the $p$-wave one, which provides more intuitive understanding for the system. Our work is useful for obtaining deeper understandings of open $p+ is$ superconducting chains on a wave function level.