三維二聚體化自旋二分之一量子反鐵磁之倪耳溫度與交錯磁化密度的普適性比尺關係

Universal scaling of Néel temperature and staggered magnetization density of three dimensional dimerized spin-1/2 quantum antiferromagnets

譚登瑞(Tan Deng-Ruei)

指導教授 ： 江府峻

國立臺灣師範大學/理學院/物理學系/博士(2019年)

https://doi.org/10.6345/NTNU201901151

摘要

本論文使用蒙地卡羅模擬對三維二聚體化自旋 1/2 反鐵磁海森堡模型做研究計算，其中使用非常有效率的隨機數列展開演算法，並且從適當的物理量和分析方法來計算倪耳溫度 $T_N$、交錯磁化密度 $M_s$ 和 $T^{star}$。在不同的非無序的三維二聚體化自旋 1/2 海森堡模型中，先前文獻上的理論計算發現了 $T_N$ 和基態的 $M_s$ 存在著 3 個普適性比尺關係，有些也和 $ extrm{TlCuCl}_3$ 的實驗結果相符。這篇論文研究已發現的普適性比尺關係在無序模型上是否成立，並且考慮其他不同的非無序二聚體化海森堡模型。我們的計算結果不但確認普適性比尺關係在無序系統依然成立，還發現其中 2 個普適性比尺關係可以根據晶格點上的自旋與周圍自旋有較強自旋耦合的總數來做分類。

關鍵字

量子蒙地卡羅 ； 反鐵磁 ； 海森堡模型

並列摘要

In this thesis, we use quantum Monte Carlo method to study three-dimensional (3D) spin-1/2 antiferromagnetic Heisenberg models. By employing every efficient algorithm, namely the stochastic series expansion (SSE), we calculate the Néel temperature $T_N$, the staggered magnetization density $M_s$, the spinwave velocity $c$, and $T^{star}$ of these systems. It is established theoretically that there are three universal scaling relations between $T_N$ and $M_s$ for 3D clean spin models. Particularly, some of the predictions are consistent with the experimental results. Motivated by this, we have simulated 3D quantum spin models with certain kinds of quenched disorder and have found that these three universal scaling relations are valid for disordered systems. Finally, by simulating several clean 3D models, we also show that two of these scaling relations can be classified by the number of strong antiferromagnetic couplings touching a spin.

並列關鍵字

quantum Monte Carlo ； antiferromagnet ； Heisenberg model

參考文獻

1. Greven, M., Birgeneau, R. J., Endoh, Y., Kastner, M. A., Matsuda, M., Shirane, G. Neutron scattering study of the two-dimensional spinS=1/2 square-lattice Heisenberg antiferromagnet Sr2CuO2Cl2. Zeitschrift für Physik B Condensed Matter, 96(4):465-477, Dec 1995.

2. Chakravarty, Sudip and Halperin, Bertrand I. and Nelson, David R. Low-temperature behavior of two-dimensional quantum antiferromagnets. Phys. Rev. Lett., 60:1057—1060, Mar 1988.

3. Haldane, F. D. M. O(3) Nonlinear σ Model and the Topological Distinction between Integer- and Half-Integer-Spin Antiferromagnets in Two Dimensions. Phys. Rev. Lett., 61:1029—1032, Aug 1988.

4. Reger, J. D. and Young, A. P. Monte Carlo simulations of the spin-1/2 Heisenberg antiferromagnet on a square lattice. Phys. Rev. B, 37:5978—5981, Apr 1988.

5. Chakravarty, Sudip and Halperin, Bertrand I. and Nelson, David R. Two-dimensional quantum Heisenberg antiferromagnet at low temperatures. Phys. Rev. B, 39:2344—2371, Feb 1989.