1. Chen Ahai and Gao Xianlong
Pure Mott phase in the fermion-Hubbard model with spatially varying tunneling
Chen Ahai and Gao Xianlong
Department of Physics, Zhejiang Normal University, Jinhua, , China

2. >Introduction
It is feasible for us to realize Mott phase in optical lattices with atoms (bosons or fermions) trapped in a harmonic external potential.
the Mott phase is always surrounded by metallic phase.
The phase transformation of general formed hubbard model with harmonic external potential in optical lattices.

3. >The Model
A pure Mott phase can be realized in system with spatially varying tunneling.
Fermion-Hubbard model with spatially varying tunneling:
Tunneling of atoms in optical lattices described by fermion-Hubbard model with spatially varying tunneling.
Tunneling of trapped atoms in optical lattices described by Hubbard model with harmonic external potential.
The calculations here are performed using the DMRG method.

4. >Results Parameters: U=4, L=70, =-2~6.9. Density distribution.
correlation functions.
Density distribution
The Fourier transformation of Spin correlation function.
The Fourier transformation of Charge correlation function.

5. (superfluid+Mott phase)
>Phases
Vacuum
Mix
(vacuum+superfluid)
Superfluid
(superfluid+Mott phase)
Pure Mott phase
(superfluid+band)
band
The width of Mott phase and the relevant positions of various phases.

6. >Phase diagram and scaling
Phase diagram as a function of chemical potential and on-site interactions U.
Phase diagram as a function of t/U and
The fluctuation of system with length up to 600.