Emergent space in quantum many-body systems

Under certain circumstances, collective fluctuations in strongly correlated quantum many-body systems may behave as if they are propagating in a spacetime which has one more dimension than the original spacetime. In this case, it is possible to understand the original system using a dual `holographic' description defined in an emergent spacetime with one higher dimension. Although there are non-trivial evidences that support the duality in specific examples constructed from the superstring theory, so far there has been no systematic way to identify dual descriptions for general quantum many-body systems. In this project, we will search for a prescription to construct dual descriptions for general systems, based on the idea to view the duality as 'quantum renormalization group' where the couplings of a theory become dynamical variables instead of being mere constants. Furthermore, we will try to uncover the hidden `quantum order' of those systems that exhibit the property of an emergent space, namely those systems that admit a classical description in an emergent spacetime, by examining the structure of long range entanglements. This project will help understand the precise content of the duality and generalize the duality to a wider range of quantum many-body systems, including condensed matter systems.