  We use bosonic field theories and the infinite system density matrix
renormalization group (iDMRG) method to study infinite strips of fractional
quantum Hall (FQH) states starting from microscopic Hamiltonians.
Finite-entanglement scaling allows us to accurately measure chiral central
charge, edge mode exponents and momenta without finite-size errors. We analyze
states in the first and second level of the standard hierarchy and compare our
results to predictions of the chiral Luttinger liquid ($\chi$LL) theory. The
results confirm the universality of scaling exponents in chiral edges and
demonstrate that renormalization is subject to universal relations in the
non-chiral case. We prove a generalized Luttinger's theorem involving all
singularities in the momentum-resolved density, which naturally arises when
mapping Landau levels on a cylinder to a fermion chain and deepens our
understanding of non-Fermi liquids in 1D.
