Chiral Luttinger liquids and a generalized Luttinger's theorem in fractional quantum Hall edges via finite-entanglement scaling

TL;DR

This paper employs bosonic field theories and iDMRG to study fractional quantum Hall edges, confirming universal scaling laws and establishing a generalized Luttinger's theorem that links momentum singularities to non-Fermi liquid behavior.

Contribution

It introduces a universal relation in non-chiral cases and validates the universality of edge scaling exponents in fractional quantum Hall states.

Findings

Confirmed universality of edge scaling exponents

Established a generalized Luttinger's theorem for FQH edges

Demonstrated universal relations in non-chiral renormalization

Abstract

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.