P.W. Anderson said " More is different ". It says the macroscopic quantum phenomena such as superfluids, superconductors, quantum anti-ferromagnetism, fractional quantum Hall states, etc emerge as the number of interacting particles gets more and more. However, he left the question how these emergent quantum or topological phenomena change under different inertial frames. In this colloquium, we try to address this outstanding problem.

We propose there is an emergent space-time corresponding to any emergent quantum phenomenon, especially near a quantum/topological phase transition (QPT).  We demonstrate this new emergent space-time structure by studying one of the simplest QPTs:Superfluid (SF)-Mott transitions of interacting bosons in a square lattice observed in a frame moving with a constant velocity $ v $ relative to the underlaying lattice.

By constructing effective actions and performing microscopic calculations on a lattice, we find that the new emergent space-time leads to several new effects in the moving frame such as the change of the ground state (the Mott phase near the QPT may turn into a SF phase, but not the other way around ), the rising of the KT transition temperature, the change of the condensation momentum, the sign reverse of the Doppler shift in the excitation spectrum relative to the bare velocity $ v $, the emergence of new class of QPTs, etc. Contrast to the Doppler shifts in a relativistic quantum field theory, Unruh effects in an accelerating  observer,emergent curved space-time from the Sachdev-Ye-Kitaev model are made.

Finally, we show that despite these effects are hard to observe in real materials, but could be detected in cold atoms loaded in an optical lattice.