Local two-body parent Hamiltonians for the entire Jain sequence

TL;DR

This paper constructs local two-body Hamiltonians for Jain states in the fractional quantum Hall effect, demonstrating their unique stabilization, edge mode correspondence, and emergent symmetries.

Contribution

It introduces a systematic method to derive local parent Hamiltonians for all unprojected Jain states, revealing their zero mode structure and underlying symmetries.

Findings

Successfully stabilizes Jain states with local two-body interactions.

Reproduces edge conformal field theory mode counting.

Identifies an emergent SU(n) symmetry in the states.

Abstract

Using an algebra of second quantized operators, we develop local two-body parent Hamiltonians for all unprojected Jain states at filling factor $n/(2n{\sf p}+1)$, with integer $n$, and (half-)integer ${\sf p}$. We rigorously establish that these states are uniquely stabilized and that zero mode counting reproduces mode counting in the associated edge conformal field theory. We further establish an associated "entangled Pauli principle" describing these states and associated zero mode spaces, as well as an emergent SU($n$) symmetry.