Many-Body Dephasing in Long-range Transverse-field Ising Chain with Trapped Ions

We investigate how a closed interacting quantum many-body system dephases as a function of time. We analyse the persistent temporal fluctuations after a quantum quench of a tunable long-range interacting transverse-field Ising Hamiltonian, which is realized with a trapped-ion quantum simulator. The one dimensional transvese-filed Ising chain has long-range power-law interactions. In the small coupling exponent regime, the properties of the system are closely related to the integrable Hamiltonian with global spin-spin coupling. Based on the eigenstate thermalization hyperthesis (ETH), we develop a non-perturbative method to get the analytical expresssion for the temopral fluctuations. The analytical expression for the temporal fluctuations predicts the exponential suppression of temporal fluctuations with increasing system size, which is consistent with our measurement data.