论文标题
研究沮丧的一维自旋1/2系统的量子阶段的机器学习方法
Machine learning approach to study quantum phases of a frustrated one dimensional spin-1/2 system
论文作者
论文摘要
挫败感驱动的量子波动导致许多外来阶段在基础状态下，研究这些量子相变是凝结物理学中最具挑战性的研究领域之一。在这里，使用主要组件分析（PCA）研究了一个沮丧的Heisenberg $ J_1-J_2 $ spin-1/2链的型号spin-1/2链，$ j_1 $ $ j_1 $，下一个最近的交换互动$ j_2 $，这是一种无监督的机器学习技术。在这种方法中，对于不同的$ J_2/J_1 $，地面状态（GS）和第一个激发状态（FES）的最可能的自旋配置（MPSC）用作PCA中的输入来构建共同变量矩阵。计算了共同变量矩阵$ p_1（J_2/j_1）$的最大特征值的“量化主组件”，并且表明$ p_1（j_2/j_1）$的性质和变化可以准确预测GS中GS中的相位过渡和脱粒。从GS的MPSC中计算出的$ P_1（J_2/J_1）$只能在GS中显示出脱落的签名，而从FES的MPSC中计算出的$ P_1（J_2/J_1）$，捕获了无间隙的旋转液体（GSL） - Dimer相位（GSL） - Dimer相过渡和所有模型系统。我们表明，以$ J_2/J_1 \约0.241 $为$ p_1（J_2/j_1）的$ p_1（j_2/j_1）$表示GSL-二聚体相变的速度，而其扭结却给出了GS脱发的签名。 FES的前两个主要成分的散点图显示了不同阶段的不同带形成。
Frustration driven quantum fluctuation leads to many exotic phases in the ground state and study of these quantum phase transitions is one of the most challenging areas of research in condensed matter physics. Here, a frustrated Heisenberg $J_1-J_2$ model of spin-1/2 chain with nearest exchange interaction $J_1$ and next nearest exchange interaction $J_2$ is studied using the principal component analysis (PCA) which is an unsupervised machine learning technique. In this method most probable spin configurations (MPSC) of ground-state (GS) and first excited state (FES) for different $J_2/J_1$ are used as the input in PCA to construct the co-variance matrix. The `quantified principal component' of the largest eigenvalue of co-variance matrix $p_1(J_2/J_1)$ is calculated and it is shown that the nature and variation of $p_1(J_2/J_1)$ can accurately predict the phase transitions and degeneracies in the GS. The $p_1(J_2/J_1)$ calculated from the MPSC of GS can only exhibit the signature of degeneracies in the GS, whereas, $p_1(J_2/J_1)$ calculated from MPSC of FES captures the gapless spin liquid (GSL)-dimer phase transition as well as all the degeneracies of the model system. We show that jump in $p_1(J_2/J_1)$ of FES at $J_2/J_1 \approx 0.241$, indicates the GSL-dimer phase transition, whereas its kinks give the signature of the GS degeneracies. The scatter plot of first two principal components of FES shows distinct band formation for different phases.
