论文标题
梳子晶格的关键特性
Critical properties of a comb lattice
论文作者
论文摘要
在本文中，我们研究了梳子晶格上海森堡自旋1/2模型的临界特性 - 牙齿有限的1D链装饰的一维骨架 - 牙齿。我们通过复制晶格几何形状的梳子张量网络来解决问题。我们观察到梳子上的状态之间的基本差异，每个牙齿的位置均匀数量和奇数，这类似于Spin-1/2梯子中的偶数效应。牙齿上的梳子始终是至关重要的，不仅沿着牙齿，而且沿着骨干，这会导致正交方向的两个关键方案之间的竞争。此外，我们表明，在弱背骨中，激发能量尺度限制为$ 1/（nl）$，而不是$ 1/n $或$ 1/l $典型的1D系统。对于弱主链中的牙齿，系统也对应于一个长度$ l $的截断临界链的集合，而在强骨架极限中，每个牙齿的一个旋转形成骨干，因此，临界牙齿的有效长度是一个较短的位置，$ l-1 $。令人惊讶的是，这两个制度是通过一个跨越两个最近的邻居牙齿的状态连接的，有效长度为2升$。
In this paper we study the critical properties of the Heisenberg spin-1/2 model on a comb lattice -- a 1D backbone decorated with finite 1D chains -- the teeth. We address the problem numerically by a comb tensor network that duplicates the geometry of a lattice. We observe a fundamental difference between the states on a comb with even and odd number of sites per tooth, which resembles an even-odd effect in spin-1/2 ladders. The comb with odd teeth is always critical, not only along the teeth, but also along the backbone, which leads to a competition between two critical regimes in orthogonal directions. In addition, we show that in a weak-backbone limit the excitation energy scales as $1/(NL)$, and not as $1/N$ or $1/L$ typical for 1D systems. For even teeth in the weak backbone limit the system corresponds to a collection of decoupled critical chains of length $L$, while in the strong backbone limit, one spin from each tooth forms the backbone, so the effective length of a critical tooth is one site shorter, $L-1$. Surprisingly, these two regimes are connected via a state where a critical chain spans over two nearest neighbor teeth, with an effective length $2L$.
