论文标题
临界自由铁链中的对称分辨的纠缠熵
Symmetry-resolved entanglement entropy in critical free-fermion chains
论文作者
论文摘要
对称分辨的rényi纠缠熵是密度矩阵$ρ$的每个对称扇区的rényi纠缠熵。已知该实验相关的数量具有丰富的理论联系与形成场理论（CFT）。对于一个关键的自由屈服链的家族，我们使用Toeplitz的决定因素理论提出了严格的基于晶格的缩放性能。我们认为具有微观u（1）对称性的一类临界量子链；每条链的能量描述低于$ n $ subseless dirac fermions。对于密度矩阵，$ρ_A$，$ l $相邻站点的子系统，我们计算了大型$ l $渐近扩展中的主要条款，对对称分辨的rényi纠缠熵。这是从$ρ_a$的充电时刻的大$ l $扩展中进行的； we derive $tr(e^{i αQ_A} ρ_A^n) = a e^{i α\langle Q_A\rangle} (σL)^{-x}(1+O(L^{-μ}))$, where $a, x$ and $μ$ are universal and $σ$ depends only on the $N$ Fermi momenta.我们表明，指数$ x $对应于CFT分析中的期望。错误项$ o（l^{ - μ}）$与字段理论预测$ O（l^{ - 2μ}）$一致，但弱。但是，使用有关相关toeplitz决定因素的进一步结果和猜想，我们发现与CFT操作员的扩展非常同意。
The symmetry-resolved Rényi entanglement entropy is the Rényi entanglement entropy of each symmetry sector of a density matrix $ρ$. This experimentally relevant quantity is known to have rich theoretical connections to conformal field theory (CFT). For a family of critical free-fermion chains, we present a rigorous lattice-based derivation of its scaling properties using the theory of Toeplitz determinants. We consider a class of critical quantum chains with a microscopic U(1) symmetry; each chain has a low energy description given by $N$ massless Dirac fermions. For the density matrix, $ρ_A$, of subsystems of $L$ neighbouring sites we calculate the leading terms in the large $L$ asymptotic expansion of the symmetry-resolved Rényi entanglement entropies. This follows from a large $L$ expansion of the charged moments of $ρ_A$; we derive $tr(e^{i αQ_A} ρ_A^n) = a e^{i α\langle Q_A\rangle} (σL)^{-x}(1+O(L^{-μ}))$, where $a, x$ and $μ$ are universal and $σ$ depends only on the $N$ Fermi momenta. We show that the exponent $x$ corresponds to the expectation from CFT analysis. The error term $O(L^{-μ})$ is consistent with but weaker than the field theory prediction $O(L^{-2μ})$. However, using further results and conjectures for the relevant Toeplitz determinant, we find excellent agreement with the expansion over CFT operators.
