论文标题
相互作用的热玻色子的Renyi熵大$ n $近似
Renyi Entropy of Interacting Thermal Bosons in Large $N$ Approximation
论文作者
论文摘要
使用基于Wigner函数的方法，我们研究了子系统$ a $ a $ a玻色子系统的Renyi熵，该系统与局部排斥潜力相互作用。假定完整的系统在温度$ t $和密度$ρ$的情况下处于热平衡状态。对于$ {\ cal u}（n）$对称模型，我们表明，可以通过有效的非相互作用系统来理解该系统在大$ n $限制中的Renyi熵，该系统具有空间变化的平均场电位，必须一致地自我确定。 Renyi熵是两个术语的总和：（a）该有效系统的Renyi熵，以及（b）有效系统和原始翻译不变系统之间的热能能量差，缩放为$ t $。我们确定在马鞍点近似中的自我一致方程。我们使用这种形式主义来查看晶格上的一个和二维的玻璃气体。在这两种情况下，潜在的概况都是广场井的概况，在子系统$ a $和外部的一个不同值中占据一个值。在密度密度相关长度的规模上，子系统$ a $边界附近的空间有所不同。相互作用对纠缠熵密度的影响取决于潜在的障碍与温度和峰值在中等温度下的峰值，而高温和低温方案则由非相互作用的答案主导。
Using a Wigner function based approach, we study the Renyi entropy of a subsystem $A$ of a system of Bosons interacting with a local repulsive potential. The full system is assumed to be in thermal equilibrium at a temperature $T$ and density $ρ$. For a ${\cal U}(N)$ symmetric model, we show that the Renyi entropy of the system in the large $N$ limit can be understood in terms of an effective non-interacting system with a spatially varying mean field potential, which has to be determined self consistently. The Renyi entropy is the sum of two terms: (a) Renyi entropy of this effective system and (b) the difference in thermal free energy between the effective system and the original translation invariant system, scaled by $T$. We determine the self consistent equation for this effective potential within a saddle point approximation. We use this formalism to look at one and two dimensional Bose gases on a lattice. In both cases, the potential profile is that of a square well, taking one value in the subsystem $A$ and a different value outside it. The potential varies in space near the boundary of the subsystem $A$ on the scale of density-density correlation length. The effect of interaction on the entanglement entropy density is determined by the ratio of the potential barrier to the temperature and peaks at an intermediate temperature, while the high and low temperature regimes are dominated by the non-interacting answer.
