Exact numerical approach to hard-core bosons on one-dimensional lattices

We describe a recently developed exact numerical approach that allows to study ground state properties and the non-equilibrium dynamics of hard-core bosons confined on 1D lattices. It is based on the Jordan-Wigner transformation and enables to analyze large system sizes such that scaling properties typical for the thermodynamic limit can be observed. We apply this exact treatment to study the off-diagonal behavior of the one-particle density matrix in systems confined by harmonic potentials. We also analyze the non-equilibrium dynamics of an initial Fock state of hard-core bosons which is allowed to evolve freely.