Particle Partition Entanglement After a Quantum Quench

在这个项目中，我们将研究相互作用粒子的量子猝灭后纠缠熵的动力学和增长，目的是了解粒子统计在孤立量子系统接近热平衡过程中所起的作用。虽然之前的工作已经研究了空间模二分下的纠缠，但我们建议研究粒子二分下的纠缠，它捕捉到相同巡回粒子子集之间的非局域和潜在的长程量子关联。这种类型的纠缠没有外部强加的长度或时间尺度，并且已经被证明对处于领先阶的粒子统计很敏感。我们预计，传统的空间纠缠在熄灭后的范例--从边界律增长到饱和，在一个广泛的值上，时间尺度由空间分区的大小决定--将针对粒子划分进行修改。在这里，我们希望揭示在本征态热化过程中，由于涨落和粒子统计引起的纠缠是如何从预猝灭的基态演化出来的。我们将结合互补的大尺度精确对角化技术和非平衡玻色化计算，研究量子猝灭引起的粒子分割纠缠熵动力学。具体地说，我们将研究无自旋晶格费米子的一维模型，并改变最近邻的排斥相互作用，以在Luttinger液体内熄灭，并在Luttinger液体和绝缘电荷密度波之间的量子相变中进行调谐。我们还将研究弱配对超导体(相当于一维空间中的Luttinger液体)和强配对超导体之间的量子相变。强配对超导体由紧密束缚对组成，在系统稳定所需的排斥次近邻耦合存在的情况下，由吸引近邻耦合的强度控制。粒子分割纠缠熵应该在这里提供令人兴奋的新信息，因为粒子的有效数量和它们的统计在这个转变过程中都会发生变化。

In this project will investigate the dynamics and growth of entanglement entropy after a quantum quench of interacting particles with the goal of understanding the role played by particle statistics during the approach of an isolated quantum system to thermal equilibrium. While previous work has explored the entanglement under a spatial mode bipartition, we propose to study entanglement under a particle bipartition, which captures non-local and potentially long-range quantum correlations between subsets of identical itinerant particles. This type of entanglement has no externally imposed length or time scales and has been shown to be sensitive to particle statistics at leading order. We expect that the conventional paradigm of spatial entanglement after a quench -- growth from a boundary-law to saturation at an extensive value with a time-scale set by the size of the spatial subregion -- will be modified for particle partitions. Here we expect to uncover how entanglement due to fluctuations and particle statistics evolves out of the pre-quench ground state during eigenstate thermalization.We will study particle partition entanglement entropy dynamics due to quantum quenches by combining complementary large scale exact diagonalization techniques with non-equilibrium bosonization calculations. Specifically, we will study one dimensional models of spinless lattice fermions and vary the nearest neighbor repulsive interactions to quench within the Luttinger liquid phase and to tune across the quantum phase transition between a Luttinger liquid and an insulating charge density wave. We will also investigate the quantum phase transitions between a weak pairing superconductor (equivalent to a Luttinger liquid in one spatial dimension) and a strong pairing superconductor consisting of tightly bound pairs, controlled by the strength of an attractive nearest neighbour coupling in the presence of a repulsive next-nearest neighbor coupling needed to stabilize the system. The particle partition entanglement entropy should provide exciting new information here, as both the effective number of particles and their statistics changes across this transition.