 The numerical method is efficient in simulating real-time dynamics or calculations of ground states using imaginary-time evolution or isentropic interpolations between a target Hamiltonian and a Hamiltonian with an already-known ground state.The computational time scales linearly with the system size, hence many-particles systems in 1D can be investigated.A useful feature of the TEBD algorithm is that it can be reliably employed for time evolution simulations of time-dependent Hamiltonians, describing systems that can be realized with cold atoms in optical lattices, or in systems far from equilibrium in quantum transport.