横向磁场中LiHoF4的微扰量子蒙特卡罗研究
Perturbative Quantum Monte Carlo Study of LiHoF4 in a Transverse Magnetic Field
摘要：
P.B.查克拉博蒂{ \it等人}，Phys. Rev. B { \bf 70}，144411（2004））在外部横向磁场$B_x$中对LiHoF $_4$ Ising磁性材料的研究显示出与实验结果的差异，即使对于量子波动小的小$B_x$也是如此。这种差异持续渐近接近经典的铁磁体顺磁体相变。在本文中，我们数值重新研究的温度$T$，与横向场相图的LiHoF $_4$在弱$B_x$制度。在这个制度下，从一个有效的低能量自旋1/2描述的LiHoF $_4$，我们应用累积展开推导出一个有效的依赖于温度的经典哈密顿量，包括微扰的小量子涨落附近的经典相变在$B_x=0$。利用这个有效的经典哈密顿量，我们通过经典的蒙特卡罗模拟研究了$B_x-T$的相图.特别是，我们调查的各种效果，可能是在以前的QMC结果和实验之间的差异的来源的相图的影响。例如，我们考虑两种不同的方式处理的长程偶极-偶极相互作用，并探讨如何修改$B_x-T$相图时，使用不同的微观晶体场哈密顿量。我们的工作的主要结论是，我们完全重现以前的QMC结果在小$B_x$。不幸的是，我们探索的微观哈密顿量的修改都不能提供一个$B_x-T$相图兼容的小半经典$B_x$制度的实验。
英文摘要：
P.B. Chakraborty {\it et al.}, Phys. Rev. B {\bf 70}, 144411 (2004)) study of the LiHoF$_4$ Ising magnetic material in an external transverse magnetic field $B_x$ show a discrepancy with the experimental results, even for small $B_x$ where quantum fluctuations are small. This discrepancy persists asymptotically close to the classical ferromagnet to paramagnet phase transition. In this paper, we numerically reinvestigate the temperature $T$, versus transverse field phase diagram of LiHoF$_4$ in the regime of weak $B_x$. In this regime, starting from an effective low-energy spin-1/2 description of LiHoF$_4$, we apply a cumulant expansion to derive an effective temperature-dependent classical Hamiltonian that incorporates perturbatively the small quantum fluctuations in the vicinity of the classical phase transition at $B_x=0$. Via this effective classical Hamiltonian, we study the $B_x-T$ phase diagram via classical Monte Carlo simulations. In particular, we investigate the influence on the phase diagram of various effects that may be at the source of the discrepancy between the previous QMC results and the experimental ones. For example, we consider two different ways of handling the long-range dipole-dipole interactions and explore how the $B_x-T$ phase diagram is modified when using different microscopic crystal field Hamiltonians. The main conclusion of our work is that we fully reproduce the previous QMC results at small $B_x$. Unfortunately, none of the modifications to the microscopic Hamiltonian that we explore are able to provide a $B_x-T$ phase diagram compatible with the experiments in the small semi-classical $B_x$ regime.
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