This dataset contains low-energy spectra and eigenvectors of two (1+1)-dimensional Quantum Field Theory models, the sine-Gordon (SG) and the double sine-Gordon (DSG) model, for a representative choice of parameter values. The data were computed using the Truncated Conformal Space Approach (TCSA), which is a Hamiltonian truncation method. Parameters: Cosine frequencies: β = 2.49239 for SG and β1 = 1.01066 and β2 = 2.49239 for DSG Dimensionless (mass)⨉(system size) parameter (m: first SG breather mass, L: system size): mL = 0.01, 0.1, 1, 2, 5 TCSA details: truncation basis: free massless boson CFT with Dirichlet boundary conditions, restricted to the ground state symmetry sector truncation cutoff (maximum CFT energy shell): 42 basis size: 85674 The spectra correspond to the full list of eigenvalues of the truncated Hamiltonian matrices in increasing order, and the eigenvectors correspond to matrices of dimensions 5173⨉5173, corresponding to the components of the lowest 5173 energy levels in the lowest 5173 basis states (the best convergent part of the eigenvector matrix at the top left corner). Each eigenvector corresponds to a column of the above matrices, in the same order as the eigenvalues. Format: Python NumPy .npy files The filenames are of the form: descriptor_model_mLx.npy where: descriptor = "Spectrum" or "Eigenvectors" model = "SG" or "DSG" x = 0.01, 0.1, 1, 2 or 5 (mL value)

Funding information: Slovenian Research Agency (ARRS) Grants N1-0109 and P1-0402 ERC Advanced Grant 694544 – OMNES