  The occurrences of collective quantum states, such as superconductivity (SC)
and charge- or spin-densitywaves (CDWs or SDWs), are among the most fascinating
phenomena in solids. To date much effort has been made to explore the interplay
between different orders, yet little is known about the relationship of
multiple orders of the same type. Here we report optical spectroscopy study on
CDWs in the rare-earth tri-telluride compounds RTe3 (R = rare earth elements).
Besides the prior reported two CDW orders, the study reveals unexpectedly the
presence of a third CDW order in the series which evolves systematically with
the size of R element. With increased chemical pressure, the first and third
CDW orders are both substantially suppressed and compete with the second one by
depleting the low energy spectral weight. A complete phase diagram for the
multiple CDW orders in this series is established.
