pure mott phase in the fermion-hubbard model with spatially varying tunneling
DESCRIPTION
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. >Introduction. - PowerPoint PPT PresentationTRANSCRIPT
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