Abstract: The classical simulation of quantum field theories is a challenging problem. We will present a new method for the study of 1 et 1D quantum field theory models, built upon Hamiltonian truncation and tensor network techniques, which is suitable for the study of low-energy eigenstates and out-of-equilibrium dynamics. Applications of the new method to the sine-Gordon and massive Schwinger model demonstrate that, despite its relatively high computational cost, it dramatically improves precision compared to exact diagonalisation results, allowing the study of so far unexplored regimes of the models’ phase diagram and of the emergence of equilibrium after a quantum quench.