Ground state wavefunction of the quantum Frenkel-Kontorova model

TL;DR

This paper calculates the ground state wavefunction of the quantum Frenkel-Kontorova model using quantum Monte Carlo, revealing a transition from extended to localized states as coupling increases, indicating remnants of classical transition in quantum regime.

Contribution

It provides the first detailed quantum Monte Carlo analysis of the ground state wavefunction in the FK model, highlighting quantum effects on classical phase transitions.

Findings

Wavefunction crosses over from extended to localized at a critical coupling.

Quantum fluctuations smear out the classical transition but remnants remain.

Transition behavior is characterized in the quantum regime.

Abstract

The wavefunction of an incommensurate ground state for a one-dimensional discrete sine-Gordon model -- the Frenkel-Kontorova (FK) model -- at zero temperature is calculated by the quantum Monte Carlo method. It is found that the ground state wavefunction crosses over from an extended state to a localized state when the coupling constant exceeds a certain critical value. So, although the quantum fluctuation has smeared out the breaking of analyticity transition as observed in the classical case, the remnant of this transition is still discernible in the quantum regime.