Method to Observe Anomaly of Magnetic Susceptibility for Quantum Spin Systems

TL;DR

This paper introduces a new method using the fourth derivative of the lowest energy eigenvalue to detect phase transition anomalies in quantum spin systems, demonstrating its effectiveness over traditional susceptibility measurements.

Contribution

The paper presents a novel approach employing the fourth derivative of energy eigenvalues to identify high-order phase transitions in quantum spin systems, validated through numerical analysis.

Findings

Anomaly of magnetic susceptibility $$ observed at zero magnetization.

Fourth derivative $A$ provides a clearer anomaly detection than $$.

Method reveals high-order (fourth order) phase transition.

Abstract

We propose a new method for studying the anomaly of magnetic susceptibility $\chi$ that indicates a phase transition for quantum spin systems. In addition, we introduce the fourth derivative $A$ of the lowest energy eigenvalue per site with respect to magnetization, that is, the second derivative of $\chi^{-1}$. To verify the validity of this method, we apply it to an $S=1/2$ XXZ antiferromagnetic chain. The lowest energy of the chain is calculated by numerical diagonalization. As a result, the anomaly of $\chi$ and $A$ exists at zero magnetization. That of $A$ is easier to observe than that of $\chi$, which indicates that the observation of $A$ is a more efficient method to evaluate an anomaly than that of $\chi$. The observation of $A$ reveals an anomaly that shows the high order phase transition, namely, the fourth order phase transition. Our method is helpful for analyzing critical phenomena.