  Entanglement or modular Hamiltonians play a crucial role in the investigation
of correlations in quantum field theories. In particular, in 1+1 space-time
dimensions, the spectra of entanglement Hamiltonians of conformal field
theories (CFTs) for certain geometries are related to the spectra of the
physical Hamiltonians of corresponding boundary CFTs. As a result, conformal
invariance allows exact computation of the spectra of the entanglement
Hamiltonians for these models. In this work, we perform this computation of the
spectrum of the entanglement Hamiltonian for the free compactified boson CFT
over a finite spatial interval. We compare the analytical results obtained for
the continuum theory with numerical simulations of a lattice-regularized model
for the CFT using density matrix renormalization group technique. To that end,
we use a lattice regularization provided by superconducting quantum electronic
circuits, built out of Josephson junctions and capacitors. Up to non-universal
effects arising due to the lattice regularization, the numerical results are
compatible with the predictions of the exact computations.
