---
abstract: 'In this article, we derive the fermionic formalism of Hamiltonians as well as corresponding excitation spectrums and states of Calogero-Sutherland(CS), Laughlin and Halperin systems, respectively. In addition, we study the triangular property of these Hamiltonians and prove the integrability in these three cases.'
address:
- 'Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing, China 100190'
- 'State Key Laboratory of Theoretical Physics, Beijing, China 100190'
- 'Institute of Theoretical Physics, Beijing University of Technology, Beijing, China 100124'
- 'Department of Mathematics, Jilin University, Changchun, China 130012'
- 'School of Mathematics Sciences, Capital Normal University, Beijing, China 100048'
- |
    Beijing Center for Mathematics and Information Interdisciplinary Sciences,\
    Beijing, China 100048
author:
- 'Li-Qiang Cai'
- 'Li-Fang Wang'
- 'Jian-Feng Wu'
- Jie Yang
- Ming Yu
title: 'Fermionization, Triangularization and Integrability'
---

Calogero-Sutherland ,Jack polynomial ,CFT ,FQHE ,integrability ,fermionization ,triangularization

02.10.Ox ,02.30.Ik ,05.30.Pr ,05.45.Yv

Introduction and Results\[sec:Introduction\]
============================================

In the area of many body physics, fractional quantum Hall effects (FQHEs) and integrable models, are two fruitful and important classes. Many researchers believe these two are connected in a hundred and one ways. [@azuma1994explicit; @bergere2000composite; @bernevig2008model; @estienne2012conformal; @ha1994exact; @zhang1989effective; @zhang1992chern] Plenty of efforts have been dedicated to find 