Method to Observe Anomaly of Magnetic Susceptibility for Quantum Spin Systems

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.

12pages, 27 figures

References in corpus (3)

• Numerical-Diagonalization Study of Spin Gap Issue of the Kagome Lattice Heisenberg Antiferromagnet
• Quantum Lattice Model Solver $\mathcal{H}\Phi$
• Gapless Spin Excitations in the $S=1/2$ Kagome- and Triangular-Lattice Heisenberg Antiferromagnets

Cited by in corpus (2)

• Exact results for nonlinear Drude weights in the spin-1/2 XXZ chain
• Fine structure of the nonlinear Drude weights in the spin-1/2 XXZ chain