The magnetic susceptibility of exchange-disordered antiferromagnetic finite chains

TL;DR

This paper investigates how exchange disorder affects the low-temperature magnetic susceptibility of finite antiferromagnetic spin chains, revealing distinct behaviors for small chains and universal scaling in the thermodynamic limit.

Contribution

It demonstrates that different exchange distributions cause qualitatively different low-temperature susceptibilities in small chains and explores the transition to universal behavior as chain length increases.

Findings

Distinct low-temperature behaviors for different exchange distributions in small chains

Universal scaling of susceptibility in the thermodynamic limit

Potential use of magnetic measurements to characterize quantum computer hardware

Abstract

The low-temperature behavior of the static magnetic susceptibility $\chi(T)$ of exchange-disordered antiferromagnetic spin chains is investigated. It is shown that for a relatively small and even number of spins in the chain, two exchange distributions which are expected to occur in nanochains of P donors in silicon lead to qualitatively distinct behaviors of the low-temperature susceptibility. As a consequence, magnetic measurements might be useful to characterize whether a given sample meets the requirements compatible with Kane's original proposalfor the exchange gates in a silicon-based quantum computer hardware. We also explore the dependence of $\chi(T)$ on the number of spins in the chain as it increases towards the thermodynamic limit, where any degree or distribution of disorder leads to the same low-temperature scaling behavior. We identify a crossover regime where the two distributions of disorder may not be clearly differentiated, but the characteristic scaling of the thermodynamic limit has not yet been reached.