臺灣博碩士論文加值系統

在此篇論文裏，我們利用量子蒙地卡羅演算法對二維竹篩晶系上，半整數自旋海森堡XYZh模型做深入的數值模擬計算研究。 近期理論分析對於XYZh模型這樣的一個挫折系統之研究提出了具有實現Z2拓撲有序之量子自旋液態的可能性。 在數值模擬研究方面，近期對於XYZh模型在竹篩晶格上的計算發現了一個在極低溫仍具有磁無序性的特殊物質態。 這種極低溫仍保有磁無序的特性使其被認為極有可能就是理論上預測的Z2拓撲有序之量子自旋態。 然而目前研究仍沒有直接證據支持此推論。 此篇論文之研究即針對這樣的一個磁無序物質態做深入的數值探討。 我們對此態的拓撲熵以及熱力學熵之量子蒙卡計算結果指出此態不具有拓撲有序，即不為先前理論預測的Z2拓撲有序之量子自旋液態。 而熱力學熵計算結果指向此態在極低溫依然為具有古典行為的自旋冰態。 在對XYZh模型更深入的理論分析，我們發現其存在非典型的微擾拮抗機制使得量子微擾效應對系統的古典行為做了強化。 此現象在我們的量子模擬計算結果中得到了驗證。 這種強化古典行為的非典型量子效應是一個非常稀少的例子。 此機制的發現為量子磁性系統提出了一個新的研究方向。

We study the spin-1/2 Heisenberg XYZh model on a kagome lattice with quantum Monte Carlo (QMC) simulation. Recently, the model is proposed to host the Z2 quantum spin liquid (QSL) with a Z2 topological order. Numerical studies found a quantum kagome ice state which lacks long-range order. This suggests the possibility for the state to be a Z2 QSL. However, no direct evidence of Z2 QSL is shown. Here, we carefully examine the XYZh model. By measuring the topological entanglement entropy using quantum Monte Carlo simulation, we find that, contrary to previous beliefs, the state has no Z2 topological order. Instead, the system behaves like a classical kagome ice down to a very low temperature. Our theoretical analysis indicates that an intricate competition of the off-diagonal and non-trivial diagonal perturbation contributions suppresses the quantum energy scale. This leads to a quasi-degenerate picture where the system remains classical. The scenario is supported with the measurement of hexagon fractions using QMC. This is a rare example of a quantum model that remains classical down to a very low temperature that is due to quantum tunneling effect. The mechanism opens a way to engineer quantum-to-classical crossover in quantum magnets.

口試委員會審定書 iii
誌謝 v
摘要 vii
Abstract ix
1 Introduction 1
1.1 XYZh model on kagome lattice 2
1.1.1 Classical limit 2
1.1.2 XXZ model with parameter J± /= 0 3
1.1.3 The disordered QKI states in parameter J±± /= 0 5
1.2 The motivation of this work 5
2 Methods 9
2.1 Stochastic Series Expansion 9
2.1.1 Representation 9
2.1.2 Update scheme 12
2.1.3 SSE applied to XYZh model on kagome lattice 13
2.2 Parallel Tempering 15
2.3 Replica trick for Renyi entropy 17
2.4 Wang-Landau method 20
3 Results 27
3.1 Topological entanglement entropy 27
3.2 Thermal entropy 29
3.3 h - J± - J±± phase diagram 31
4 Degenerate perturbation theory 35
4.1 Formulation 35
4.2 J± as perturbation 37
4.3 J±± as perturbation 38
4.4 Quantum enhancement of classical behavior in QKI 43
4.4.1 Numerical evidence for the enhancement 43
5 Conclusion and outlook 47
Bibliography 49

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