Supersolid-superfluid phase separation in the extended Bose-Hubbard model

Recent studies have suggested a new phase in the extended Bose-Hubbard model in one dimension at integer filling [1,2]. In this work, we show that this new phase is phase-separated into a supersolid and superfluid part, generated by mechanical instability. Numerical simulations are performed by means of the density matrix renormalization group algorithm in terms of matrix product states. In the phase-separated phase and the adjacent homogeneous superfluid and supersolid phases, we find peculiar spatial patterns in the entanglement spectrum and string-order correlation functions and show that they survive in the thermodynamic limit. In particular, we demonstrate that the elementary excitatio…