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.