AI 中文总结
本文研究隧穿耦合Luttinger液体的纠缠动力学，推导任意耦合方案下的相关信息论量解析表达式，分析零温、有限温及慢耦合下的纠缠特性，将非平衡场论纠缠动力学研究扩展至场空间划分与混合初始态。
AI 中文摘要
纠缠动力学不仅取决于量子系统的划分方式，还关键取决于跨该划分的相互作用结构。对于局域相互作用系统的空间二分划分，纠缠在边界附近产生，随后向体内部传播；相比之下，当两个扩展量子场沿整个长度局域耦合时，相互作用会处处跨场空间划分，从而在整个系统中产生关联。本文研究由Luttinger液体理论描述的两个无间隙一维量子多体系统之间的纠缠动力学，这些系统初始时解耦，制备于零温或有限温，之后沿其长度均匀激活含时隧穿相互作用。在高斯近似下，我们推导了任意耦合方案下对数负性、互信息和Rényi熵的一般解析表达式。零温下，纠缠呈现早期幂律增长，其指数仅由隧穿方案的第一个非零导数决定；耦合饱和后，我们得到信息论量的精确长时间平均值，并表征了关联如何随温度和最终耦合强度缩放。我们还分析了对于相对于本征系统时标非常缓慢的方案，互信息和对数负性如何趋近绝热极限。本工作将非平衡场论中的纠缠动力学研究扩展到了场空间划分和混合初始态的情形。
英文摘要
Entanglement dynamics depend not only on how a quantum system is partitioned, but critically on how interactions across that partition are structured. For a spatial bipartition of a locally interacting system, entanglement is generated near the boundary and then propagates into the bulk. By contrast, when two extended quantum fields are coupled locally along their entire length, the interaction crosses the field-space partition everywhere, and this generates correlations throughout the system. Here, we study the entanglement dynamics between two gapless one-dimensional quantum many-body systems described by Luttinger liquid theory. The systems are initially decoupled and prepared at zero or finite temperature, after which a time-dependent tunneling interaction is activated uniformly along their length. Within a Gaussian approximation, we derive general analytical expressions for the logarithmic negativity, mutual information, and Rényi entropies under arbitrary coupling protocols. At zero temperature, entanglement displays an early-time power-law growth whose exponent is fixed solely by the first non-null derivative of the tunneling protocol. Once the coupling saturates, we obtain exact long-time averages of the information-theoretic quantities and characterise how the correlations scale with temperature and the final coupling strength. We also analyse how mutual information and logarithmic negativity approach the adiabatic limit for a very slow protocol with respect to intrinsic system timescale. This work extends the study of entanglement dynamics in nonequilibrium field theory to field-space partitions and mixed initial states.
Comments45 pages, 8 figures
