Is it possible that the speed of sound in some strange quantum material is faster than the speed of light in vacuum If we believe the spacetime structure(including the limit of speed) could emerge from some vacuum structure(such as string-net condensation),then, is it possible that the speed of mode of excitation in some strange quantum material could be faster than the speed of light in vacuum? Notice, is the speed of light in vacuum not in material. From the view point above, if there is no such material, the fact would look strange. After all, the amount of quantum material is far more than the vacuum that could be seen as a special material if it has some structure. 
 A: The most common reaction you will find is that the speed of sound has to be below the causality speed-limit $c$ (which is also the speed of light in vacuum). However, in the case of wave motion there are two (or more) different speeds that may be of interest. The two main ones are the phase velocity $\omega/k$ and the group velocity $d\omega/dk$. There is no speed limit on the phase velocity.
I haven't looked into this, but I think it is possible to construct media where the phase velocity of sound would be high, by combining two or more ordinary media. I don't know about group velocity, but in ordinary circumstances a sound wave has a causal influence at the group velocity so this suffices to say it could not exceed $c$.
A: No. It is not possible. 
In the name of the physical constant called the "speed of light in a vacuum", the "in a vacuum" part adds nothing to the conversation and is basically anachronistic (it was named before the photon understanding of light and special relativity were invented).
In the sense used in regard to the speed of light, you statement that:

the amount of quantum material is far more than the vacuum that could
  be seen as a special material if it has some structure.

suggests a misunderstanding. A "vacuum" in this sense is defined to mean nothing. It isn't a material and it doesn't have structure.
The lack of any linkage between the speed of light and any medium is perhaps best illustrated mathematically by the Lorentz transformation in which the physical constant "c" is used whether the Lorentz transform involves a massless particle or a massive one, and which does not have a factor incorporating any particular medium.
Photons always travel at the speed of light at the fundamental particle scale (as do all fundamental particles with zero "rest mass", i.e. photons, gluons and hypothetically, gravitons).
Light only appears to travel more slowly through a non-vacuum medium because it is getting bounced around on different indirect routes between fundamental particles that make up the medium, and because it is being absorbed and re-emitted (usually) multiple times. What is called the speed of light in a non-vacuum medium is just a phenomenological estimation of the average impact of these factors in a simplified system with so many sub-particles that the law of averages makes the actual result very close to the average result for a system of that type.
When light passes through glass or water, the photon that comes out of the medium at the far end will generally not be the original photon that went in (although this is not really a meaningful distinction, because all photons of the same wave length, helicity, and polarization are identical).
If you are a picture person, the same thing is explained with diagrams, to which I don't have copyright privileges, here. Previous answers at Physics.SE to very similar questions are here.
The tags for this question suggest that you are wondering if quantum entanglement could play a part in a medium that would allow light to traverse it faster than the speed of light, and the answer to that is also no. The process of light passing through a medium is not one in which quantum entanglement is established.
