Metal to Wigner-Mott insulator transition in two-leg ladders

TL;DR

This paper theoretically investigates the continuous metal to Wigner-Mott insulator transition in two-leg ladders, revealing how symmetry breaking and spin gaps depend on fractional filling, with implications for two-dimensional systems.

Contribution

It introduces a new theoretical framework for understanding continuous Wigner-Mott transitions in ladder systems, highlighting the role of fractional filling and spin sector behavior.

Findings

Continuous transition with symmetry breaking at fractional filling.

Spin gap opens for odd m, remains gapless for even m.

Presence of a gapless charge-neutral mode across the transition.

Abstract

We study theoretically the quantum phase transition from a metal to a Wigner-Mott insulator at fractional commensurate filling on a two-leg ladder. We show that a continuous transition out of a symmetry-preserving Luttinger liquid metal is possible where the onset of insulating behavior is accompanied by the breaking of the lattice translation symmetry. At fillings $\nu = 1/m$ per spin per unit cell, we find that the spin degrees of freedom also acquire a gap at the Wigner-Mott transition for odd integer $m$. In contrast for even integer $m$, the spin sector remains gapless and the resulting insulator is a ladder analog of the two-dimensional spinon surface state. In both cases, a charge neutral spinless mode remains gapless across the Wigner-Mott transition. We discuss physical properties of these transitions, and comment on insights obtained for thinking about continuous Wigner-Mott transitions in two-dimensional systems which are being studied in moire materials.