Entangled Pauli Principles: the DNA of Quantum Hall Fluids

TL;DR

This paper introduces entangled Pauli principles to rigorously analyze fractional quantum Hall states with Landau level mixing, connecting microscopic solutions to effective field theories and revealing new entanglement structures.

Contribution

It develops a formalism for entangled Pauli principles that incorporate Landau level mixing, enabling microscopic analysis of quantum Hall phases beyond single Landau level models.

Findings

Exact solutions for Jain-221 state derived from microscopic Hamiltonian.

Root-level entanglement exhibits AKLT-type MPS structure with SU(2) symmetry.

Insights into braiding statistics and edge theory from microscopic solutions.

Abstract

A formalism is developed for the rigorous study of solvable fractional quantum Hall parent Hamiltonians with Landau level mixing. The idea of organization through "generalized Pauli principles" is expanded to allow for root level entanglement, giving rise to "entangled Pauli principles". Through the latter, aspects of the effective field theory description become ingrained in exact microscopic solutions for a great wealth of phases for which no similar single Landau level description is known. We discuss in detail braiding statistic, edge theory, and rigorous zero mode counting for the Jain-221 state as derived from a microscopic Hamiltonian. The relevant root-level entanglement is found to feature an AKLT-type MPS structure associated with an emergent SU(2) symmetry.