Decohering the Fermi liquid: A dual approach to the Mott Transition

TL;DR

This paper introduces a dual theoretical approach to the Mott transition in two-dimensional electron systems, emphasizing the suppression of Fermi surface shape fluctuations and revealing a quantum spin liquid state with a spinon Fermi surface.

Contribution

It develops a coarse-grained, vortex-based method to describe the Mott transition and the resulting spin liquid, offering an alternative to slave particle formulations.

Findings

The Mott insulator is a quantum spin liquid with a spinon Fermi surface.

Suppression of Fermi surface shape fluctuations leads to a spin liquid state.

The approach provides a new perspective on the physics of the Mott transition.

Abstract

We present a theoretical approach to describing the Mott transition of electrons on a two dimensional lattice that begins with the low energy effective theory of the Fermi liquid. The approach to the Mott transition must be characterized by the suppression of density and current fluctuations which correspond to specific shape deformations of the Fermi surface. We explore the nature of the Mott insulator and the corresponding Mott transition when these shape fluctuations of the Fermi surface are suppressed without making any a prior assumptions about other Fermi surface shape fluctuations. Building on insights from the theory of the Mott transition of bosons, we implement this suppression by identifying and condensing vortex degrees of freedom in the phase of the low energy electron operator. We show that the resulting Mott insulator is a quantum spin liquid with a spinon fermi surface coupled to a U(1) gauge field which is usually described within a slave particle formulation. Our approach thus provides a coarse-grained treatment of the Mott transition and the proximate spin liquid that is nevertheless equivalent to the standard slave particle construction. This alternate point of view provides further insight into the novel physics of the Mott transition and the spin liquid state that is potentially useful. We describe a generalization that suppresses spin anti-symmetric fluctuations of the Fermi surface that leads to a spin-gapped charge metal previously also discussed in terms of slave particle constructions.