Particle Partition Entanglement After a Quantum Quench

• Applicant: Professor Dr. Bernd Rosenow
• Subject Area: Theoretical Condensed Matter Physics
• Term: from 2018 to 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 404758601

• Final Report Year: 2020

Final Report Abstract

The time evolution of an initial quantum state after a sudden change of interaction strength leads to an asymptotic steady state, which may exhibit local properties that are described by an ensemble with finite thermodynamic entropy density. This is a result of entanglement between macroscopic spatial subregions that grows due to the propagation of quasiparticles. Studying entanglement between groups of particles is an alternative approach to considering entanglement between spatial subregions. Such particle entanglement is based on n-point correlation functions and does not impose an external length scale on the system. Here we analyze fermions after an interaction quantum quench in one spatial dimension and demonstrate that the steady state entropy density accumulated via entanglement dynamics is equivalent under either a spatial or particle bipartition. The monotonically decreasing scaling of the particle entanglement denstity with increasing n highlights that small values of n could be useful for placing an upper bound. Even the diagonal components of the 2-point correlation function can be employed to construct a diagonal ensemble density matrix of non-interacting bosons and compute the von Neuman entropy density. Since density-density correlations in a quantum gas are readily accessible with current experimental technologies, this presents a complimentary route to the experimental measurement of the Renyi entropy in non-equilibrium quantum systems and highlights the dynamical transmutation of entanglement to thermodynamic entropy under time evolution that underlies our current framework of quantum statistical mechanics. This project provided an opportunity for Prof. Del Maestro to spend his sabbatical visiting the University of Leipzig and working in close collaboration with the group of Prof. Rosenow. It led to a number of novel scientific projects at the forefront of quantum many-body systems as well as training and exchange experiences that would not otherwise have been possible.

Publications

• Rényi Generalization of the Accessible Entanglement Entropy, Phys. Rev. Lett. 121, 150501 (2018)
  Hatem Barghathi, Chris M. Herdman, and Adrian Del Maestro
  
• Theory of Liquid Film Growth and Wetting Instabilities on Graphene, Phys. Rev. Lett. 120, 236802 (2018)
  Sanghita Sengupta, Nathan S. Nichols, Adrian Del Maestro, and Valeri N. Kotov
  
• Universal Entanglement Growth After a Quantum Quench
  Adrian Del Maestro, Hatem Barghathi and Bernd Rosenow