我們在有限溫度的二維反鐵磁量子海森堡JQ3模型下，設定J鍵、Q鍵兩種晶格鍵結交互作用，利用第一原理蒙地卡羅模擬，在Q鍵強度與J鍵強度比值Ｑ/Ｊ為臨界狀態(Ｑ/Ｊ)_c及不同的系統溫度之下，計算系統各物理量，以得到系統普適常數(S(π,π))/(χ_s T) 、 (χ_u c^2)/T 、 (ρ_s L)/c對系統溫度T倒數(β)的變化，以此探討當物理系統從Néel 相變至 Valence-bond solid的物理性質。我們所研究的JQ3模型共有三種，其中兩種：正方晶格平行Q鍵模型及蜂巢Q鍵模型在文獻中屬於二階相變，另一種正方晶格斜排Q鍵屬於一階相變。從前兩種模型的模擬結果，我們得到相當足夠且與過去文獻一致的證俱，並且可支持該兩種模型的相變為連續性相變，另外對比這三種模型的結果，我們也得到可提供當JQ3模型物理系統在臨界相變時，系統屬於一階相變或二階相變的判斷標準。
本論文部分章節已發表於 Chinese Journal of Physics 77 (2022) 1598–1609.

In order to study the Quantum phase transition from the Néel phase to the valence-bond solid, we study with 2D-antiferromagnetic Quantum Heisenberg JQ3 model at finite temperature by the first principles Quantum Monte Carlo simulation. We calculate the universal Quantities (S(π,π))/(χ_s T) 、 (χ_u c^2)/T 、 (ρ_s L)/c and consider these Quantities as functions of the inverse temperature(β).The simulations are conducted at the critical points (Q/J)_c. Three types of JQ3 models, namely the square-ladder model, the honeycomb, and the square-stagger models are studied. In the literature, the first two models are known to have second order phase transition, and the last one is likely to have a first order phase transition.
The results shown in our study provide numerical evidence to support the outcomes established in literature. Moreover, our results can be a criterion to distinguish second order phase transitions from first order phase transitions for the exotic criticalities of JQ-type models.

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