Bandwidth-control vs. doping-control Mott transition in the Hubbard model

We reinvestigate the bandwidth-control and doping-control Mott transitions (BCMT and DCMT) from a spin liquid Mott insulator to a Fermi liquid metal based on the slave-rotor representation of the Hubbard model,\cite{Florens} where the Mott transitions are described by softening of bosonic collective excitations. We find that the nature of the insulating phase away from half filling is different from that of half filling in the respect that a charge density wave coexists with a topological order (spin liquid) away from half filling because the condensation of vortices generically breaks translational symmetry in the presence of "dual magnetic fields" resulting from hole doping while the topological order remains stable owing to gapless excitations near the Fermi surface. Performing a renormalization group analysis, we discuss the role of dissipative gauge fluctuations due to the Fermi surface in both the BCMT and the DCMT.