Exotic Gapless Mott Insulators of Bosons on Multi-Leg Ladders

TL;DR

This paper provides evidence for a novel gapless insulating phase of bosons on multi-leg ladders, characterized by two gapless modes and power-law correlations, supported by variational and DMRG calculations.

Contribution

It introduces a new gapless insulating phase in multi-leg bosonic ladders with a specific model and proposes a wave function that matches numerical results, advancing understanding of exotic quantum phases.

Findings

Identification of a gapless insulating phase with two modes

Excellent agreement between variational Monte Carlo and DMRG results

Discussion of extensions to other N-leg and layered systems

Abstract

We present evidence for an exotic gapless insulating phase of hard-core bosons on multi-leg ladders with a density commensurate with the number of legs. In particular, we study in detail a model of bosons moving with direct hopping and frustrating ring exchange on a 3-leg ladder at $\nu=1/3$ filling. For sufficiently large ring exchange, the system is insulating along the ladder but has two gapless modes and power law transverse density correlations at incommensurate wave vectors. We propose a determinantal wave function for this phase and find excellent comparison between variational Monte Carlo and density matrix renormalization group calculations on the model Hamiltonian, thus providing strong evidence for the existence of this exotic phase. Finally, we discuss extensions of our results to other $N$-leg systems and to $N$-layer two-dimensional structures.