Chaos and entanglement growth in a system of two connected Bosonic optical lattices

We study the entanglement entropy of eigenstates of a bipartite many-body quantum system as a function of the coupling strength, with both subsystems exhibiting chaos. Random matrix theory has been used to analytically predict entropy increase as a function of a transition parameter when two chaotic quantum subsystems (namely, quantum kicked rotors) become increasingly connected [1, 2]. This parameter, which depends on the strength of the coupling between the subsystems, defines universal scaling laws for entropy growth in the case of subsystems with no additional conserved quantities. The question is whether entanglement growth in many-body systems follows similar scaling laws, or if it is affected by internal symmetries in the system that arise from the two-body operators in the Hamiltonian. The Hubbard model for bosonic particles in a periodic optical lattice (Bose-Hubbard ring) is a many-body system that exhibits chaos for specific parameter regimes and provides a test case for the study of entanglement growth. We simulated a pair of connected Bose-Hubbard rings that are chaotic, with disorder in the lattice parameters to eliminate geometric symmetries, leaving only particle conservation as the remaining symmetry when the rings are uncoupled. Preliminary results suggest that for small coupling, the entanglement entropy is suppressed compared to interacting kicked rotors, but it increases more rapidly and catches up with the predicted entropy after the coupling has sufficiently increased. This seems to indicate that the symmetry imposed by particle-number conservation in either subsystem is gradually broken and speeds up the growth of entropy until it has caught up with the random matrix prediction.



[1] S. L. Srivastava, S. Tomsovic, A. Lakshminarayan, R. Ketzmerick, A. Bäcker, Phys. Rev. Lett. 116, 054101

[2] S. Tomsovic, A. Lakshminarayan, S. L. Srivastava, A. Bäcker, Phys. Rev. E 98, 032209