论文标题
临界量子旋转链中的新兴普遍性：纠缠virasoro代数
Emergent universality in critical quantum spin chains: entanglement Virasoro algebra
论文作者
论文摘要
纠缠熵和纠缠光谱已被广泛用于表征延长的多体系统中的量子纠缠。鉴于系统的纯净状态和区域分为$ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ $ a $的$ schmidt〜values $λ_α$。在本文中，我们将注意力提请注意$ schmidt〜vectors $或eigenVectors $ |v_α\ rangle $ $ρ_a$。我们考虑了临界量子旋转链的基态，其低能/长距离物理是由新兴的保形场理论（CFT）描述的。我们表明，施密特矢量$ |v_α\ rangle $显示出紧急的通用结构，对应于边界CFT的Virasoro代数的实现（原始CFT的手性版本）。的确，我们建立加权总和$ h_n $的晶格哈密顿密度$ h_ {j，j+1} $ a $ a $ a $ $ a $，并表明矩阵元素$ \ langlev_αh_n| v_v_ | v_ | v_ {α'} \ rangle $是通用的。更具体地说，这些矩阵元素是由$ h_n^{\ tiny \ text {cft}} = \ frac 1 2（l_n + l_ { - n}）$的类似表达式给出的，其中$ l_n $是$ l_n $的（一份）virasoro Generators。我们使用关键的ISIN量子自旋链和其他（自由屈光度等效）模型来确认结果。
Entanglement entropy and entanglement spectrum have been widely used to characterize quantum entanglement in extended many-body systems. Given a pure state of the system and a division into regions $A$ and $B$, they can be obtained in terms of the $Schmidt~ values$, or eigenvalues $λ_α$ of the reduced density matrix $ρ_A$ for region $A$. In this paper we draw attention instead to the $Schmidt~ vectors$, or eigenvectors $|v_α\rangle$ of $ρ_A$. We consider the ground state of critical quantum spin chains whose low energy/long distance physics is described by an emergent conformal field theory (CFT). We show that the Schmidt vectors $|v_α\rangle$ display an emergent universal structure, corresponding to a realization of the Virasoro algebra of a boundary CFT (a chiral version of the original CFT). Indeed, we build weighted sums $H_n$ of the lattice Hamiltonian density $h_{j,j+1}$ over region $A$ and show that the matrix elements $\langle v_αH_n |v_{α'}\rangle$ are universal, up to finite-size corrections. More concretely, these matrix elements are given by an analogous expression for $H_n^{\tiny \text{CFT}} = \frac 1 2 (L_n + L_{-n})$ in the boundary CFT, where $L_n$'s are (one copy of) the Virasoro generators. We numerically confirm our results using the critical Ising quantum spin chain and other (free-fermion equivalent) models.
