Algorithm for simulation of quantum many-body dynamics using dynamical coarse graining

An algorithm for simulation of quantum many-body dynamics having su(2) spectrum-generating algebra is developed. The algorithm is based on the idea of dynamical coarse-graining. The original unitary dynamics of the target observables, the elements of the spectrum-generating algebra, is simulated by a surrogate open-system dynamics, which can be interpreted as weak measurement of the target observables, performed on the evolving system. The open-system state can be represented by a mixture of pure states, localized in the phase-space. The localization reduces the scaling of the computational resources with the Hilbert space dimension n by factor n^{3/2}/ln n compared to conventional sparse-matrix methods. The guidelines for the choice of parameters for the simulation are presented and the scaling of the computational resources with the Hilbert space dimension of the system is estimated. The algorithm is applied to the simulation of the dynamics of systems of 2*10^4 and 2*10^6 cold atoms in the double-well trap, described by the two-sites Bose-Hubbard model.