A lot of information about (1+1)-dimensional quantum many-body systems may be revealed in studying their energy spectra. Their investigation provides the key to distinguish different phases of matter and to search for signatures of continuous phase transitions, which are of great interest in modern condensed matter physics due to the emerging conformal symmetry. This emergence allows a description of the critical behavior in terms of a conformal field theory (CFT). In this master thesis a short introduction to the framework of CFTs is given and their appearance in the low lying energy spectra of critical systems is explained. This is accomplished by analyzing the energy spectrum of the (1+1)-dimensional transverse field Ising (TFI) model using analytical and numerical tools. The main part of the thesis is concerned with the numerical simulation of a more complicated model: The QFT of interacting, bosonic, spinless particles, the theory. The Fock space Hamiltonian truncation (FSHT) technique introduces an ultraviolet (UV) energy cutoff allowing for an exact diagonalization (ED) of the truncated, finite dimensional Hamiltonian matrix and offers additional renormalization group improvements. Using the FSHT method the energy spectrum of this strongly coupled QFT is numerically computed in a non-perturbative, controlled way.