Large effects of boundaries on spin amplification in spin chains

TL;DR

This paper demonstrates that boundary conditions critically influence spin amplification in spin chains, with even minimal boundary modifications causing significant changes in the system's macroscopic behavior, especially in the thermodynamic limit.

Contribution

The study introduces a semiclassical analytical framework to understand how boundary conditions induce bifurcations in Hilbert space, affecting spin chain dynamics.

Findings

Boundary conditions significantly alter spin amplification behavior.

A single boundary coupling can change the physical properties of the system.

Semiclassical methods effectively analyze boundary effects in large chains.

Abstract

We investigate the effect of boundary conditions on spin amplification in spin chains. We show that the boundaries play a crucial role for the dynamics: A single additional coupling between the first and last spins can macroscopically modify the physical behavior compared to the open chain, even in the limit of infinitely long chains. We show that this effect can be understood in terms of a "bifurcation" in Hilbert space that can give access to different parts of Hilbert space with macroscopically different physical properties of the basis functions, depending on the boundary conditions. On the technical side, we introduce semiclassical methods whose precision increase with increasing chain length and allow us to analytically demonstrate the effects of the boundaries in the thermodynamic limit.