# Elementary Excitations in Fractional Quantum Hall Effect from Classical Constraints

## TL;DR

This paper extends classical local exclusion constraints to construct and analyze elementary excitations in fractional quantum Hall states, revealing topological equivalences and new insights into exotic quantum phases.

## Contribution

It introduces a method to build quasiholes and quasielectrons from classical constraints, connecting different FQH phases and exotic states.

## Key findings

- Quasielectron excitations are topologically equivalent to composite fermion results.
- LEC construction provides a new perspective on FQH phase connections.
- Constructed microscopic wave functions for various quasiparticles.

## Abstract

Classical constraints on the reduced density matrix of quantum fluids in a single Landau level, termed as local exclusion conditions (LECs) [B. Yang, arXiv:1901.00047], have recently been shown to characterize the ground state of many FQH phases. In this work, we extend the LEC construction to build the elementary excitations, namely quasiholes and quasielectrons, of these FQH phases. In particular, we elucidate the quasihole counting, categorize various types of quasielectrons, and construct their microscopic wave functions. Our extensive numerical calculations indicate that the undressed quasielectron excitations of the Laughlin state obtained from LECs are topologically equivalent to those obtained from the composite fermion theory. Intriguingly, the LEC construction unveils interesting connections between different FQH phases and offers a novel perspective on exotic states such as the Gaffnian and the Fibonacci state.