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

TL;DR

This paper presents a novel theoretical framework linking a two-dimensional fermion model undergoing a Mott transition to a Double Lattice Chern-Simons theory via Hilbert space mapping, offering new insights into the transition's nature.

Contribution

It introduces an explicit Hilbert space mapping between the fermionic model and Chern-Simons theory, advancing the understanding of the Mott transition through integrability and algebraic methods.

Findings

Hilbert space mapping between fermion model and Chern-Simons theory

Characterization of the transition via ground state modification

New tools for probing Mott transition properties

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).