A transformation that accounts for the universality found in Ref. [1] concerning the finite energy behavior of dynamical correlation functions of both integrable and non-integrable 1D correlated systems is used to generate from the pseudo-fermion dynamical theory of the integrable 1D Hubbard model [2] a corresponding renormalized theory with additional electron finite-range interactions [3,4]. The obtained renormalized theory is used to describe the experimental spectral lines in the angle resolved photoemission spectroscopy of the 1D quantum line defects in the 2D van der Waals layered semiconductor MoSe2 [3] and of the quasi-1D compound TTF-TCNQ [4]. The theoretical predictions refer to finite-energy ω windows in the vicinity of the cusps of the observed spectral lines. The dispersions and (k, ω)-plane weight distributions of such two systems are found to exactly follow those predicted by the non-integrable finite-range renormalized model with the exponent α for the density of states suppression, |ω| α, being given by α ≈ 0.73 − 0.78 for the MoSe2 line defects [3] and α ≈ 0.53 for TTF-TCNQ [4]. The latter value is thirteen times larger than that predicted by the simple 1D Hubbard model, α ≈ 0.04, for which α ∈ [0, 1/8] [5].

[1] A. Imambekov and L. I. Glazman Science 323 228 (2009).
[2] J. M. P. Carmelo and T. Cadez Nuclear Physics B 914, 461 (2017).
[3] Y. Ma, H. C. Diaz, J. Avila, C. Chen, V. Kalappattil, R. Das, M.-H. Phan, T. Cadez, J. M. P. Carmelo, M. C. Asensio, and M. Batzill  Nature Communications 8, 14231 (2017).
[4] J. M. P. Carmelo, T. Cadez, M. Sing, and R. Claessen (Work in progress).
[5] M. Sing, U. Schwingenschlogl, R. Claessen, P. Blaha, J. M. P. Carmelo, L. M. Martelo, P. D. Sacramento, M. Dressel, and C. S. Jacobsen, Physical Review B 68 125111 (2003) .

* J. M. P. Carmelo, Universidade do Minho, Portugal