U(1) symmetry breaking in one-dimensional Mott insulator studied by the   Density Matrix Renormalization Group method
  A new type of external fields violating the particle number preservation is studied in one-dimensional strongly correlated systems by the Density Matrix Renormalization Group method. Due to the U(1) symmetry breaking, the ground state has fluctuation of the total particle number, which implies injection of electrons and holes from out of the chain. This charge fluctuation can be relevant even at half-filling because the particle-hole symmetry is preserved with the finite effective field. In addition, we discuss a quantum phase transition obtained by considering the symmetry-breaking fields as a mean field of interchain-hopping. 
Isao Maruyama, Tetsuji Koide and Yasuhiro Hatsugai