  We develop a package of numerical simulations implemented in MATLAB to solve
complex many-body quantum systems. We focus on widely used examples that
include the calculation of the magnetization dynamics for the closed and open
Ising model, dynamical quantum phase transition in cavity QED arrays, Markovian
dynamics for interacting two-level systems, and the non-Markovian dynamics of
the pure-dephasing spin-boson model. These examples will be useful for
undergraduate and graduate students with a medium or high background in MATLAB,
and also for researches interested in numerical studies applied to quantum
optics and condensed matter systems.
