Continuous transitions between composite Fermi liquid and Landau Fermi liquid: a route to fractionalized Mott insulators

TL;DR

This paper investigates continuous quantum phase transitions from composite Fermi liquids to Landau Fermi liquids, revealing intermediate gapless Mott insulators and potential routes to fractionalized Mott insulators, with observable signatures and implications for topological states.

Contribution

It introduces a new framework for understanding continuous transitions from CFL to Fermi liquids, including the role of neutral fermionic excitations and broader quantum fluctuations.

Findings

Identification of a gapless Mott insulator with a Fermi surface of neutral fermions.

Observation of two crossover temperature scales and resistivity jumps during the transition.

Implications for quantum critical points between non-Abelian topological states.

Abstract

One of the most successful theories of a non-Fermi liquid metallic state is the composite Fermi liquid (CFL) theory of the half-filled Landau level. In this paper, we study continuous quantum phase transitions out of the CFL state and into a Landau Fermi liquid, in the limit of no disorder and fixed particle number. This transition can be induced by tuning the bandwidth of the Landau level relative to the interaction energy, for instance through an externally applied periodic potential. We find a transition to the Landau Fermi liquid through a gapless Mott insulator with a Fermi surface of neutral fermionic excitations. In the presence of spatial symmetries, we also find a direct continuous transition between the CFL and the Landau Fermi liquid. The transitions have a number of characteristic observable signatures, including the presence of two crossover temperature scales, resistivity jumps, and vanishing compressibility. When the composite fermions are paired instead, our results imply quantum critical points between various non-Abelian topological states, including the \nu = 1/2 Moore-Read Pfaffian (Ising x U(1) topological order), a version of the Kitaev B phase (Ising topological order), and paired electronic superconductors. To study such transitions, we use a projective construction of the CFL, which goes beyond the conventional framework of flux attachment to include a broader set of quantum fluctuations. These considerations suggest a possible route to fractionalized Mott insulators by starting with FQH states and tuning the Landau level bandwidth.