Bambi Hu


DENSITY MATRIX RENORMALIZATION GROUP APPROACH TO QUANTUM FRENKEL-KONTOROVA MODEL

 
Department of Physics
Hong Kong Baptist University
Kowloon Tong
Hong Kong
Department of Physics
University of Houston
Houston, TX 77204-5005
USA

 
The Frenkel-Kontorova (FK) model describes a chain of atoms connected by harmonic springs and subjected to an external sinusoidal potential. This deceptively simple classical model however exbibits very rich and complex behaviors. The quantum version of the models is even more complicated. We've used two approaches: the coherent state approach and the density matrix renromalization group approach to study the quantum FK model. Many new and interesting features have been discovered. For example, quantum fluctuations will first renormalize the sinusoidal standard map to a saw-tooth map and change the wave function from an extended state to a localized state. However, as the effective Planck's constant is increased further, the saw-tooth map will become smoothened and the wave function will become extended again. These results may be of relevance to quantum phase transitions of cold atoms loaded in optical lattices.