Peierls-insulator Mott-insulator transition in 1D
a r X i v :c o n d -m a t /0106116v 2 [c o n d -m a t .s t r -e l ] 26 J u l 2001
Peierls-insulator Mott-insulator transition in 1D
H.Fehske a ,G.Wellein b ,A.Wei?e a ,F.G¨o hmann a ,H.B¨u ttner a ,and A.R.Bishop c
a
Physikalisches Institut,Universt¨a t Bayreuth,95440Bayreuth,Germany b
Regionales Rechenzentrum Erlangen,Universit¨a t Erlangen,91058Erlangen,Germany c
MSB262,Los Alamos National Laboratory,Los Alamos,New Mexico 87545,U.S.A.
Abstract
In an attempt to clarify the nature of the crossover from a Peierls band insulator to a Mott Hubbard insulator,we analyze ground-state and spectral properties of the one-dimensional half-?lled Holstein Hubbard model using exact diagonalization techniques.
Keywords:strongly correlated electron-phonon systems,Peierls insulator,Mott insulator In a wide range of quasi-one-dimensional ma-terials,such as MX chains,conjugated poly-mers or ferroelectric perovskites,the itineracy of the electrons strongly competes with electron-electron and electron-phonon (EP)interactions,which tend to localize the charge carriers by es-tablishing spin-density-wave and charge-density-wave ground states,respectively.Hence,at half-?lling,Peierls (PI)or Mott (MI)insulating phases are energetically favored over the metallic state.An interesting and still controversial question is whether or not only one quantum critical point separates the PI and MI phases at T =0[1].Furthermore,how is the crossover modi?ed when phonon dynamical e?ects,which are known to be of particular importance in low-dimensional ma-terials [2,3],are taken into account?
The paradigm in studies of this subject is the half-?lled Holstein-Hubbard model (HHM),de-?ned by the Hamiltonian
H =?t
i,σ
(c ?
iσc i +1σ+H.c.)+U i
n i ↑n i ↓+gω0
i,σ
(b ?i +b i )n iσ+ω0
i
b ?i b i .
(1)
Here c ?iσcreates a spin-σelectron at Wannier
site i (n i,σ=c ?iσc iσ),b ?
i creates a local phonon of frequency ω0,t denotes the hopping integral,U is the on-site Hubbard repulsion,g is a measure of the EP coupling strength,and the summation over i extends over a periodic chain of N sites.
Applying basically exact numerical meth-
ods [4],we are able to diagonalize the HHM on
?nite chains,preserving the full dynamics of the phonons.In order to characterize the ground-state and spectral properties of the HHM in dif-ferent parameter regimes,we have calculated the charge-and spin-structure factors at q =πS c (π)=14)
(2)
S s (π)=
1
N
m =0
| ψ0|?j |ψm |2
S c (π)
U/t
E k i n (g 2
ω0,U ) / E k i n (0,0)
Figure 1:Staggered charge-and spin-density cor-relations (upper panel),kinetic energy and local magnetic moment (lower panel)in the ground state of the Holstein-Hubbard model (ω0/t =1;N =8).Results are shown at g 2ω0/t =0(dia-monds),0.5(circles),and 2.0(squares).
the system is typi?ed by a charge-ordered bipo-laronic insulator rather than a traditional Peierls band insulator.The PI regime is characterized by a large (small)charge (spin)structure factor,a strongly reduced kinetic energy,and an opti-cal response that is dominated by multiphonon absorption and emission processes.
(ii)Increasing U at ?xed g ,the Peierls dimer-ization and the concomitant charge order are sup-pressed.Accordingly the system evolves from the PI to the MI regime.From our numerical data we found evidence for only one critical point U c (cf.,e.g.,the development of the optical gap in the conductivity spectra shown Fig.2).At U c ,in our ?nite system a site parity change of the ground state takes place from P =+1(PI)to P =?1(MI),and both the spin and the charge gaps are
0.00.5
1.01.5
2.0σ
r e g
0.0
0.51.01.5
σ
r e g
2
4
6
8
10
12
ω/t
0.0
0.5
1.01.5
σ
r e g
U/t=2
U/t=4
U/t=6
PI
MI
Figure 2:Optical absorption in the HHM (ω0/t =1;
N =8).Dashed lines give the integrated spectral weights S reg (ω)= ω0σreg
(ω′)dω′[normalized by S reg (∞)].
U/t P
1.84
0.24
1.7
?s (8)/t
2
+1,N
2?
1,N
2,N
2
+1,
N
2
,
N
Mott Hubbard insulating regime the optical gap is by its nature a correlation gap.It is rapidly destroyed by doping the system away from half ?lling[5].
References
[1]M.Fabrizio et al.,Phys.Rev.Lett.83,2014
(1999);
S.Qin et al.,arXiv:cond-mat/0004162;
P.Brune et al.,arXiv:cond-mat/0106007. [2] E.Jeckelmann et al.,Phys.Rev.B60,7950
(1999);
[3]H.Fehske et al.,Adv.Sol.State Phys.40,235
(2000).
[4] A.Wei?e et al.,Phys.Rev.B62,R747(2000).
[5] E.Jeckelmann,Phys.Rev.B57,7950(1998).