Critical Theory of Two-Dimensional Mott Transition: Integrability and Hilbert Space Mapping

Federico L Bottesi,Guillermo R Zemba

doi:10.4236/jmp.2015.65069

Abstract

We reconsider the Mott transition in the context of a two-dimensional fermion model with density-density coupling. We exhibit a Hilbert space mapping between the original model and the Double Lattice Chern-Simons theory at the critical point by use of the representation theory of the q-oscillator and Weyl algebras. The transition is further characterized by the ground state modification. The explicit mapping provides a new tool to further probe and test the detailed physical properties of the fermionic lattice model considered here and to enhance our understanding of the Mott transition(s).

Highlights

The physical properties of strongly correlated electron systems are difficult to predict or even to describe, mainly because of the lack of suitable reliable tools to study them
We have provided an extension of the method of integrability to a (2 + 1)-dimensional spinless fermion model with nearest neighbors Coulomb interactions, having written down an Effective Field Theory (EFT) to further study the properties of the model at the Mott transition critical point
Using the representation theory of this algebra, we have constructed a explicit mapping between the states of the original fermion model at the Mott critical point (∆ = −1) and the states of the lattice Double Chern Simons theory at coupling constant k = 1

Summary

Introduction

The physical properties of strongly correlated electron systems are difficult to predict or even to describe, mainly because of the lack of suitable reliable tools to study them. The goal of the present article is to reformulate this approach in a different, perhaps more straightforward fashion which could be useful for future developments and generalizations, and to shown that the EFT previously obtained is the corresponding (equivalent) field theory at the level of the Hilbert space at the critical point. Under this approach, we will show that, the Mott transition is characterized as a change in the ground state

Fermionic Model and Its Integrability

Conclusion