I often find out papers and textbooks that remark the ressemblance between QFT and Condensed Matter. I think that this has to do with the fact that both theories use the same tools, namely, field theory, renormalization, etc. So, is there any common interpretation or link between the mass gap in the spectrum of a quantum field theory and the band gap on materials in condensed matter?
The mass of Dirac fermions in high-energy physics is the band gap in condensed matter if we view our universe as a band insulator. Both high-energy physics and condensed matter physics use the same quantum field theory to describe particles/excitations in quantum many-body systems, so many concepts are just the same. However, in condensed matter physics, energy gaps are further divided into different types. For example, the band gap is a gap in the single-particle energy spectrum, and the Mott gap is a gap in the many-body energy spectrum. Both gaps are called "mass" in the high-energy physics.