- 學位論文
低維度無序自旋1/2海森堡模型的基態特性
Ground State Properties of Disordered Spin-1/2 Heisenberg Models in Low Dimensions
摘要
由自旋的隨機配對組成的隨機雙重相，展現了集體和普遍的臨界行為，並統治著帶有隨機耦合的反鐵磁自旋為1/2海森堡鏈的低能量物理。隨機雙重相存在於廣泛的自旋鏈中，包括在無擾動的情況下存在能隙的自旋為1的鏈。然而，儘管自旋為1/2的海森堡雙梯子與自旋為1的鏈相似，但在耦合引入隨機性時並不會轉變為隨機雙重相。即使具有極弱的鏈間耦合，無序自旋梯子仍保持在一個具有短程相關性的格里菲斯相。在此，我們利用量子蒙地卡羅模擬和強隨機場重整化群方法，研究由兩條或更多稀疏連接的鏈組成的海森堡模型的基態性質。具體而言，我們檢查了當隨機去除部分鏈間耦合時，雙梯子是否轉變為隨機雙重相。我們的目標是了解在低維自旋系統中通過增加連接性如何破壞隨機雙重相。
並列摘要
The random-singlet (RS) phase consists of random pairing of spins showing collective and universal critical behavior, which governs low-energy physics of the antiferromagnetic spin-1/2 Heisenberg chain with random couplings. The RS phases are found in a broad class of spin chains, including the spin-1 chain that is gapped in the absence of disorder. On the other hand, the spin-1/2 Heisenberg two-leg ladder, despite its similarity to the spin-1 chain, does not transform to an RS phase by introducing randomness in couplings. Even with extremely weak interchain couplings, the disordered spin ladder remains in a Griffiths phase with short-range correlations. Here, we employ quantum Monte Carlo simulations and the Strong Disorder Renormalized Group (SDRG) method to investigate the ground state properties of Heisenberg models composed of two or more chains with sparse connectivities. In particular, we examine whether there is a transition to the RS phase in a two-leg ladder when a fraction of interchain couplings are removed randomly. Our goal is to understand how the RS phase breaks down by increasing connectivities in low-dimensional spin systems.