Collapse of one-dimensional Mott Insulators due to charge fluctuation is studied by the DMRG method, where the charge fluctuation implies injection of electrons and holes from out of the system. To introduce this "doping" effect, we construct a Hamiltonian, which does not conserve a particle number but still preserves the particle-hole symmetry. Due to the U(1) symmetry breaking term, zero temperature fluctuation of the total particle number is finite even at half filling and is proportional to the inverse of the Coulomb interaction in the strong coupling.
The U(1) symmetry breaking term in the present model can be regarded as a mean field of an inter-chain hopping when we use a string type decoupling. If the interchain hopping is irrelevant, total number of the 1D system is conserved and the 1D Mott insulator is realized. Quantum phase transition collapsing the Mott gap is also discussed.
We extend the DMRG method to treat a generic fermionic system with a U(1) symmetry breaking term where its total fermion number is not conserved.
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