Density Matrix Renormalization Group study on incommensurate quantum Frenkel-Kontorova model

TL;DR

This study uses DMRG to numerically analyze the incommensurate quantum Frenkel-Kontorova model, revealing how strong quantum fluctuations alter the system's behavior and correlations, with implications for cold atom phase transitions.

Contribution

It provides the first detailed numerical investigation of the quantum Frenkel-Kontorova model using DMRG, highlighting new behaviors of the -function under strong quantum fluctuations.

Findings

Altered -function behavior in depinned state

Detailed analysis of position correlations

Potential applications to cold atom phase transitions

Abstract

By using the density matrix renormalization group (DMRG) technique, the incommensurate quantum Frenkel-Kontorova model is investigated numerically. It is found that when the quantum fluctuation is strong enough, the \emph{g}-function featured by a saw-tooth map in the depinned state will show a different kind of behavior, similar to a standard map, but with reduced magnitude. The related position correlations are studied in details, which leads to a potentially interesting application to the recently well-explored phase transitions in cold atoms loaded in optical lattices.