Particle Partition Entanglement After a Quantum Quench

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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.