I have worked quite much researching good and low-cost boost converters with very low input voltage. As tpetar pointed out, you should look if you can have a smaller input voltage range, and especially voltages below 3V gets trickier and trickier when you approach the 1V input voltage. Especially, when you want some real output power, as 5V, 600mA is 3W. It is VERY demanding specs for one-volt input! Even with efficiency of 100% the AVERAGE input current would be 3A, and switch peak currents in magnitude five times higher (at least!). And 100% efficiency is just a dream, for this kind of converters you would be lucky to get 50-85%.And that would be close to impossible at 1V input anyway due to practical available components having not ideal enough properties for such operating condition.
However, if you can manage with a lithium battery input voltage range, something around 3.5V-4V, you should be able to find many solutions. Look Maxim and Linear Technology and Texas Instruments, to mention a few. They have all nice selection tools to narrow your search.