论文标题
pyrochlore的古典和量子阶段$ s = 1/2 $磁铁与海森伯格和dzyaloshinskii-moriya互动
Classical and quantum phases of the pyrochlore $S=1/2$ magnet with Heisenberg and Dzyaloshinskii-Moriya interactions
论文作者
论文摘要
我们研究了经典和量子$ s = 1/2 $ pyrochlore晶格的基态和临界温度相图，其近距离海森伯格和dzyaloshinskii-moriya相互作用（DMI）。我们认为铁磁和抗铁磁磁性海森堡交换以及直接和间接的DMI。从经典上讲，发现了三个基础状态：全加入/全面，铁磁和本地有序的$ xy $ phase，称为$γ_5$，它显示出意外的经典u（1）堕落。发现量子零点的能量波动可以提升经典的基态堕落，并在$γ_5$制度的大多数部分中选择$ψ_3$状态。同样，经典处理的热波动，在$ t = 0^+$下选择$ψ_3$状态。相比之下，经典的蒙特卡洛（Monte Carlo）发现，对于反铁磁性海森伯格交易所（Heisenberg Heisenberg Exchange）的$ψ_2$中的$ t_c $ $ t_c $ p_c $，并从$ψ_2$过渡到$ψ_3$，以$ t_ p_ {γ_5} <t_c $从$ψ_2$过渡到$ψ_3$。同样的方法发现，该系统通过$ T_C $以$ T_C $的单个过渡订购，直接在该地区的大多数地区使用铁磁Heisenberg Exchange和间接DMI订购。 $ s = 1/2 $量子模型以$ t_c $处于$ t_c $的此类订购行为可以通过高温系列扩展来证实。为了调查$ t = 0 $量子接地状态，我们应用了伪屈光度功能重新归一化组（PFFRG）。发现直接或间接DMI的相图中的有限区域，发现纯抗磁磁性$ s = 1/2 $ HEISENBERG模型的量子顺磁相可以持续存在。我们发现，在铁磁性的边界和$γ_5$抗磁性的边界附近，系统可能会实现缺乏常规磁性的量子基态。否则，对于相图的最大部分，PFFRG找到了与经典模型相同的有序阶段。
We investigate the ground state and critical temperature phase diagrams of the classical and quantum $S=1/2$ pyrochlore lattice with nearest-neighbor Heisenberg and Dzyaloshinskii-Moriya interactions (DMI). We consider ferromagnetic and antiferromagnetic Heisenberg exchange as well as direct and indirect DMI. Classically, three ground states are found: all-in/all-out, ferromagnetic and a locally ordered $XY$ phase, known as $Γ_5$, which displays an accidental classical U(1) degeneracy. Quantum zero-point energy fluctuations are found to lift the classical ground state degeneracy and select the $ψ_3$ state in most parts of the $Γ_5$ regime. Likewise, thermal fluctuations treated classically, select the $ψ_3$ state at $T=0^+$. In contrast, classical Monte Carlo finds that the system orders at $T_c$ in the $ψ_2$ state of $Γ_5$ for antiferromagnetic Heisenberg exchange and indirect DMI with a transition from $ψ_2$ to $ψ_3$ at a temperature $T_{Γ_5} <T_c$. The same method finds that the system orders via a single transition at $T_c$ directly into the $ψ_3$ state for most of the region with ferromagnetic Heisenberg exchange and indirect DMI. Such ordering behavior at $T_c$ for the $S=1/2$ quantum model is corroborated by high-temperature series expansion. To investigate the $T=0$ quantum ground states, we apply the pseudo-fermion functional renormalization group (PFFRG). The quantum paramagnetic phase of the pure antiferromagnetic $S=1/2$ Heisenberg model is found to persist over a finite region in the phase diagram for both direct or indirect DMI. We find that near the boundary of ferromagnetism and $Γ_5$ antiferromagnetism the system may potentially realize a quantum ground state lacking conventional magnetic order. Otherwise, for the largest portion of the phase diagram, PFFRG finds the same ordered phases as in the classical model.
