Correlations and N\'eel Order of Randomly Diluted Quantum Spin Ladders

TL;DR

This study uses Monte Carlo simulations to analyze how random dilution affects correlations and Néel order in quantum spin ladders, revealing optimal doping levels and linking theoretical results to experimental observations.

Contribution

It provides the first detailed Monte Carlo analysis of correlation lengths in diluted quantum spin ladders, connecting low-temperature behavior to experimental Néel temperatures.

Findings

Correlation length peaks at specific dilution fractions

Néel temperature corresponds to constant correlation length

Enhanced two-dimensional correlations drive Néel order

Abstract

We present a Monte Carlo study of the correlation length $\xi$ of randomly diluted antiferromagnetic Heisenberg ladders, composed of two spin--1/2 chains. For weak and intermediate inter--chain couplings, $J_{\bot}/J \leq 1$, we find an enhancement of correlations that is strongest for a fraction $z^* \approx J_{\bot}/(8J)$ of dilutants. We are able to access the experimentally relevant low--temperature regime, $T/J \approx 1/500$, and find that the recently inferred N\'eel temperature of $Sr(Cu_{1-z}Zn_z)_2O_3$ corresponds to a curve of constant correlation length $\xi \approx 18$ of the single diluted ladder with $J_{\bot}/J \alt 1/2$. The primary reason for the N\'eel ordering is argued to be a strong enhancement of two--dimensional correlations due to a Cu--Sr--Cu exchange coupling of $\approx 10 meV$ in the stacking direction of the ladders.