横场ANNNI模型及其双层结构中量子Fisher-Selke序列的出现

中文摘要 AI 辅助

我们研究了方格和双层上的横场轴向次近邻伊辛（ANNNI）模型。在经典多相点κ=J2/J0=1/2处，每个将至少两个位点的域分开的直畴壁构型都是基态。畴壁是刚性的，因此可以对每个构型分别进行横场g=Γ/J0的微扰论，我们将其计算到g^8阶。量子涨落在g^2阶选择⟨3⟩（↑↑↑↓↓↓），因为靠近畴壁的自旋从虚拟翻转中获得最多的能量。结构⟨23⟩、⟨223⟩和⟨2223⟩随后在g^4、g^6和g^8阶在⟨3⟩和反相⟨2⟩之间打开，顺序与经典三维模型的Fisher-Selke序列一致。第二层比局部场的刚性化更强烈地抑制每个连续相。我们使用随机级数展开量子蒙特卡罗测试两个最宽的相，通过热力学积分比较竞争有序态的自由能，因为退火冻结了在有序转变时形成的调制。模拟将⟨3⟩楔形再现到约1%，并且在预注册测试中，⟨23⟩在七个点中的六个点稳定，第七个点通过事后运行解决。

英文摘要

We study the transverse-field axial next-nearest-neighbor Ising (ANNNI) model on the square lattice and on a bilayer. At the classical multiphase point $κ=J_2/J_0=1/2$, every configuration of straight domain walls that separates domains of at least two sites is a ground state. The walls are rigid, so perturbation theory in the transverse field $g=Γ/J_0$ can be carried out for each configuration separately, and we take it to order $g^8$. Quantum fluctuations select $\langle 3\rangle$ ($\uparrow\uparrow\uparrow\downarrow\downarrow\downarrow$) at order $g^2$, because spins next to a wall gain the most energy from virtual flips. The structures $\langle 23\rangle$, $\langle 223\rangle$ and $\langle 2223\rangle$ then open between $\langle 3\rangle$ and the antiphase $\langle 2\rangle$ at orders $g^4$, $g^6$ and $g^8$, in the order of the Fisher-Selke sequence of the classical three-dimensional model. A second layer suppresses each successive phase more strongly, beyond the stiffening of the local fields. We test the two widest phases with stochastic series expansion quantum Monte Carlo, comparing the free energies of the competing ordered states by thermodynamic integration, since annealing freezes in the modulation that forms at the ordering transition. The simulations reproduce the $\langle 3\rangle$ wedge to about 1%, and in a pre-registered test $\langle 23\rangle$ is stable at six of seven points, with the seventh resolved by post-hoc runs.

发表机构

• College of Natural Sciences, Can Tho University（芹苴大学自然科学学院）
• Identity Quantum Computing JSC（Identity量子计算股份公司）
• Faculty of Electronics and Telecommunications, University of Science, Vietnam National University Ho Chi Minh City (VNU-HCM)（越南国立大学胡志明市科技大学电子与电信学院）

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