通过正弦平方变形连接一维临界系统的远端
Connecting distant ends of one-dimensional critical systems by a sine-square deformation
摘要：
研究了具有正弦平方形变的一维量子临界自旋系统，其中哈密顿量中$x$位置的能量标度被函数$f_x = \sin^2\left[π{L}(x-1/2)]$修正，其中$L$是系统的长度.通过对纠缠熵、自旋关联函数和波函数重叠的研究，我们发现正弦平方形变极大地改变了基态几何连接的拓扑结构;虽然系统表面上有开放的边缘，但正弦平方形变连接了这些边缘，并在波函数水平上实现了周期性基态.我们的结果提出了一种新的方法来控制量子态的拓扑结构的能量标度变形。
英文摘要：
We study the one-dimensional quantum critical spin systems with the sine-square deformation, in which the energy scale in the Hamiltonian at the position $x$ is modified by the function $f_x = \sin^2\left[π{L}(x-1/2)]$, where $L$ is the length of the system. By investigating the entanglement entropy, spin correlation functions, and wave-function overlap, we show that the sine-square deformation changes the topology of the geometrical connection of the ground state drastically; Although the system apparently has open edges, the sine-square deformation links those ends and realizes the periodic ground state at the level of wave function. Our results propose a new method to control the topology of quantum states by energy-scale deformation.
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