Quantum phase transition in one-dimensional commensurate Frenkel-Kontorova model

TL;DR

This study investigates a one-dimensional quantum Frenkel-Kontorova model, revealing a quantum phase transition from pinned to sliding phases driven by quantum fluctuations, using DMRG methods.

Contribution

It provides the first detailed analysis of the quantum phase transition in the 1D commensurate Frenkel-Kontorova model with DMRG.

Findings

Identification of a quantum phase transition at a critical quantum fluctuation value

Characterization of entanglement and correlation changes across the transition

Ground state energy and energy gap behavior near the critical point

Abstract

In this paper, we have studied the one-dimensional commensurate quantum Frenkel-Kontorova model by a density-matrix renormalization group (DMRG) algorithm. The focus has been on its properties of the entanglement, the coordinate correlation, the ground state energy and the energy gap between the ground state and the first excited one. It is demonstrated that a quantum phase transition (QPT) between the pinned and the sliding phases takes place as the quantum fluctuation, measured by an effective Planck constant $\tilde\hbar$, increases to a threshold value $\tilde \hbar_c$.