Pure Mott phase in the fermion-Hubbard model with spatially varying tunneling

Chen Ahai and Gao Xianlong

Department of Physics, Zhejiang Normal University, Jinhua, 321004, China

• It is feasible for us to realize Mott phase in optical lattices with atoms (bosons or fermions) trapped in a harmonic external potential.

,, ,

†1,( . .)i i har ii i

i i i

H t c c h c U n n V n

>Introduction

• the Mott phase is always surrounded by metallic phase.

The phase transformation of general formed hubbard model with harmonic external potential in optical lattices.

>The Model

• A pure Mott phase can be realized in system with spatially varying tunneling.• Fermion-Hubbard model with spatially varying tunneling:

, 1 , 1, ,,

†

,

( . .)i i i i ii ii i i

H t c c h c U n n n

, 1 2

( 1)( 1 )

( / 2)i i

t i L it

L

• The calculations here are performed using the DMRG method.

Tunneling of trapped atoms in optical lattices described by Hubbard model with harmonic external potential.

Tunneling of atoms in optical lattices described by fermion-Hubbard model with spatially varying tunneling.

• Parameters: U=4, L=70, =-2~6.9.• Density distribution.• correlation functions.

( ) ( )

, ,

1 1( ) ( , ) ik i j ik i j

i ji j i j

S k S i j e s s eL L

( ) ( )

, ,

1 1( ) ( , ) ik i j ik i j

i ji j i j

n k n i j e c c eL L

The Fourier transformation of Spin correlation function.

The Fourier transformation of Charge correlation function.

Density distribution

VacuumVacuum

MixMix(vacuum+superfluid)(vacuum+superfluid)

SuperfluidSuperfluid

Mix Mix (superfluid+Mott phase)(superfluid+Mott phase)

Pure Mott phasePure Mott phase

Mix Mix (superfluid+Mott phase)(superfluid+Mott phase)

SuperfluidSuperfluid

Mix Mix (superfluid+band)(superfluid+band)

bandband

>Phases

The width of Mott phase and the relevant positions of various phases.

Phase diagram as a function of chemical potential and on-site interactions U.

Phase diagram as a function of t/U and . /U

The fluctuation of system with length up to 600.

>Phase diagram and scaling