论文标题
具有周期性边界条件模型
Bipartite fidelity for models with periodic boundary conditions
论文作者
论文摘要
对于给定的统计模型，双方保真$ \ MATHCAL F $是根据大小$ n $的地面之间的重叠来计算的，以及在两个子系统$ a $ a $ a $ a $ a $ a $ a $ a和$ b $上定义的地面的张量产品，$ n_a $ n_a $ n_a $和$ n_b $ with $ n_b $ with $ n_b $ with $ n_b $ n = n __b $ n =在本文中，在整个系统具有定期边界条件的情况下，我们研究了关键晶格模型的$ \ Mathcal f $。我们考虑了子系统$ a $ a $ a $ a $ a $ a $ a $ a和$ b $的两种可能选择，即定期和开放。在这两种情况下，我们在$ \ Mathcal f $的$ 1/n $扩展中得出了同条字段理论的预测，在最一般的情况下，分别与四个和五个字段的插入相对应。我们提供了两个自由用的晶格模型的$ \ Mathcal F $的晶格计算：XX旋转链和临界密集聚合物的模型。我们研究了这两个模型的晶格结果的渐近行为，并找到与保形场理论的预测一致。
For a given statistical model, the bipartite fidelity $\mathcal F$ is computed from the overlap between the groundstate of a system of size $N$ and the tensor product of the groundstates of the same model defined on two subsystems $A$ and $B$, of respective sizes $N_A$ and $N_B$ with $N = N_A + N_B$. In this paper, we study $\mathcal F$ for critical lattice models in the case where the full system has periodic boundary conditions. We consider two possible choices of boundary conditions for the subsystems $A$ and $B$, namely periodic and open. For these two cases, we derive the conformal field theory prediction for the leading terms in the $1/N$ expansion of $\mathcal F$, in a most general case that corresponds to the insertion of four and five fields, respectively. We provide lattice calculations of $\mathcal F$, both exact and numerical, for two free-fermionic lattice models: the XX spin chain and the model of critical dense polymers. We study the asymptotic behaviour of the lattice results for these two models and find an agreement with the predictions of conformal field theory.
