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

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.

7 pages, 7 figures

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• Entanglement spectroscopy of chiral edge modes in the Quantum Hall effect
• Universal chiral Luttinger liquid behavior in a graphene fractional quantum Hall point contact
• Universal signatures of Dirac fermions in entanglement and charge fluctuations
• Ergodic Edge Modes in the 4D Quantum Hall Effect
• Infinite Matrix Product States vs Infinite Projected Entangled-Pair States on the Cylinder: a comparative study
• Many-body study of a quantum point contact in the fractional quantum Hall regime at v=5/2
• Geometric entanglement in integer quantum Hall states with boundaries
• Edge reconstruction of compressible Quantum Hall fluid in the filling fraction range 1/3 to 2/3
• Second Rényi entropy and annulus partition function for one-dimensional quantum critical systems with boundaries
• Rényi entropies for one-dimensional quantum systems with mixed boundary conditions
• Collapse of edge reconstruction in compressible Quantum Hall fluid within filling fraction range 2/3 to 1