Quantum phase transition in the Frenkel-Kontorova chain: from pinned instanton glass to sliding phonon gas

TL;DR

This paper investigates a quantum phase transition in the one-dimensional Frenkel-Kontorova chain, revealing a transition from a pinned instanton glass to a sliding phonon gas as the effective Planck constant increases beyond a critical value.

Contribution

It provides the first analytical and numerical evidence of a quantum phase transition in the Frenkel-Kontorova chain from a gapped pinned phase to a gapless sliding phase.

Findings

Identification of a critical Planck constant ${ ext{hbar}_c}$ for the phase transition.

Demonstration of divergence in correlation length at the transition.

Observation of gapless phonon excitations in the sliding phase.

Abstract

We study analytically and numerically the one-dimensional quantum Frenkel-Kontorova chain in the regime when the classical model is located in the pinned phase characterized by the gaped phonon excitations and devil's staircase. By extensive quantum Monte Carlo simulations we show that for the effective Planck constant $\hbar$ smaller than the critical value $\hbar_c$ the quantum chain is in the pinned instanton glass phase. In this phase the elementary excitations have two branches: phonons, separated from zero energy by a finite gap, and instantons which have an exponentially small excitation energy. At $\hbar=\hbar_c$ the quantum phase transition takes place and for $\hbar>\hbar_c$ the pinned instanton glass is transformed into the sliding phonon gas with gapless phonon excitations. This transition is accompanied by the divergence of the spatial correlation length and appearence of sliding modes at $\hbar>\hbar_c$.