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Spin-spin correlations in the tt’-Hubbard model
T. Husslein, D. Newns, H. Mattutis, P. Pattnaik, I. Morgenstern, J. Singer, W. Fettes, C. Baur
To cite this version:
T. Husslein, D. Newns, H. Mattutis, P. Pattnaik, I. Morgenstern, et al.. Spin-spin correlations in the tt’-Hubbard model. Journal de Physique I, EDP Sciences, 1994, 4 (11), pp.1573-1576.
�10.1051/jp1:1994101�. �jpa-00247014�
Classification
Physics Abstracts 74.20
Short Communication
Spin-spin correlations in the tt'-Hubbard model
T. Husslein (~,~), D.M. Newns (~), H-G- Mattutis (~), P-C- Pattnaik (~),
I. Morgenstern (~,~), J-M- Singer (~), W. Fettes (~) and C. Baur (~)
(~) IBM Thomas J. Watson Research Center, P-O- Box 218, Yorktown Heights, NY 10598,
U-S-A-
(~) Universitàt Regensburg, Fakultàt Physik, D-93040 Regensburg, Germany
(Received 29 August 1994, received in final form 8 September 1994, accepted 13 September 1994)
Abstract. We present calculations of the tt'-Hubbard model using Quantum Monte Carlo
techniques. The parameters are chosen so that the van Hove Singularity in the density of states and the Fermi level coincide. We study the behaviour of the system with increasing Hubbard interaction U. Special emphasis is on the spin-spin correlation (SSC). Unusual behaviour for
large U is observed there and in the momentum distribution function (n(q))
The possibility of a d-wave symmetry of trie order pararneter in trie high transition temper-
ature cuprates becomes more and more evident Ill. We already reported [2] on trie coincidence
of d-wave superconductivity in trie presence of a van Hove Singularity in trie density of states, scanning trie parameter space with respect ta doping. Now we want to look in more detail into the behaviour of trie system with increasing Hubbard interaction U.
Trie model of our choice is trie tt'-Hubbard model. There an additional next-nearest neigh-
bour hopping is added to trie pure Hubbard model [3].
H = -t £ c)~cj« + h-c- + t' £ c)~cj« + h-c- + U £
n~tn~ (l)
l~,JIOE ((~ J)lOE ~
Here Ii, j) denotes trie sum over nearest neighbours, and iii, j)) denotes the sum over next-
nearest neighbour interactions; t and t' are defined to be positive. The noninteracting band
structure of the tt'-Hubbard model has saddle points at (0, x) and (x, 0), at energy -4t'.
In contrast to trie bare Hubbard model it is possible ta study the influence of a van Hove
Singularity and nesting of trie Fermi Surface mdependently. Moreover it is much simpler to
handle than trie Three-Band-Hubbard mortel [4] which bas this appealing feature too.
1574 JOURNAL DE PHYSIQUE I N°11
0 016
u=1 -
u=2 --
~ ~~~
u
Î Î-
~ ", U"4 ~~
,> ,, u=5 -w-
O.ol 2 >' '*
'.
.. ,
w
., ', ,
., 'A ,
O.ol ,? .l' a ', Î
, , , ,
>' ,','. ', '~.
~' ,~/ .' "_ ',
0 008 .',~
<'
"
', ~,
~p " n '," >' " ',
~- + ,, ',
, ',
~' ,' ,'~ '7" '' "i ',Ù '.
0006 ,' ,' n >' ', '. , .,
,j,,,x ~~,-. ,, ~~. ,
~~~~7~'
J3--
"~
." ', "Î',' Î
0 004 ~ ,,"
_. .' '.
~ '~~ "~,Î,
/.' ,,"' -+----~ ",, ", Î".
,', P' _:+ ', 'Î
0 002 ' ~,,' '~ ~, Î'
+...-- ".
, ~
,0 002
(0,0) (0,K) (K.K) j001
Fig, l. Spin-spin correlation S(q) for an 8 x 8-system for U ranging from 1 to 5, 50 particles (doping 0.21) tp = -o.22.
The Monte Carlo calculations are based on trie Projector Quantum Monte Carlo Technique.
A Projector e~~ is apphed to a test wave function (WT). For details see [si and references therein. Trie parameter 8 is trie inverse temperature, chosen to be 1/8 for ail calculations pre- sented here. We used trie Single Spin Flip update in trie calculations [6]. Stabilized Algorithms
allow trie study of trie low temperature properties I?i
There is a special emphasis on trie spm-spm correlation function S(q) S(q) =
£ e~~~~S(r) (2)
S(r) "
~ (n~1 ~il(nJ1 nJi) (3)
l~-Jl=r
m order to compare with spm-fluctuation theory [8]. There trie occurrence of d-wave su-
perconductivity is also predicted. Trie crucial point is that a large interaction U leads to a
narrow peak in trie spin-spm channel at (x, x). And this antiferromagnetic mstability leads to
superconductivity.
For our choice of parameters we found that trie phase-diagrarn of trie SSC faits into two parts with respect to U. For U below 5 we find a peak at (x, x) increasmg with U (Fig. l).
But U being above 5 (Fig. 2) reveals a drastic change. Trie peak is now splitting into two
peaks, or at least givmg a very broad mountain at (x,x). For us these are strong indications that spin fluctuations might play only a minor rote in this model.
Additionally ibis drastic change m trie SSC can be correlated to a vanishing gap m trie mo-
0 016
u=6 -
u=7 -- 0 014
~_
-~ u=8 Ha-
,"j,'
0 012 .' .' 1,
,, ~,
,d
0 01 1"
0 008
§
ce 0 006
0 004
0 002
.0 002
(0,0j 10.K) (K,Kl (0.0j
Fig. 2. Spin-spin correlation S(q) for an 8 x 8-system for U ranging from 6 to 8, 50 partiales (doping o.21) tp = -o.22.
mentum distribution function (Fig. 3).
n(q) = fle~~~~n(r) (4)
"(~) " i~)~r) (5)
Here one observes a sudden dosing of trie gap between occupied and unoccupied states going from (0, 4x/5) to (0,x) for U above 5. Whether this is due to a breakdown of Fermi Liquid theory is not yet dear.
We are aware of trie fact that trie small duster sizes mherit trie possibility of a too low resolu-
tion to detect a very narrow peak. Further simulations usmg larger system sizes are under way.
Superconducting correlations still bave large errorbars but seem to vanish for U greater than 4. When we again look at figure 1 we might connect this to a shift in the SSC-peak from about
(x, 4xlà) to (x, x) exactly. This is m good agreement to the expenmental situation [9] where
one finds the peak to be slightly off (x, x).
In conclusion we presented calculations of the tt'-Hubbard model doped nght at the van Hove. For mcreasing U we find indications that for large U the SSC is not peaking sharply at
(x, x). The system shows a closmg gap m the n(q) which might be due to a non-Fermi liquid
state. Further calculations are m progress.
1576 JOURNAL DE PHYSIQUE I N°11
2
u=0 -
u=2 --
u=3 -a-
u=5 -»-
u=6 -~-
-~ u=8 -w-
-~
'-m~",
., ,
., ", ',
08 ., ~, ',
'»", "
', '
',"
0 6
w c
[ 1 ,
,,
, ,,
, ,,
' '~
' '
' 1
', ' .
,
', __
Fig. 3. - n(q)
knowledgments.
Part
also rateful to K.A. Müller, D.J. alapino, C.C. Tsuei and M. Imada
for eferences
[Ii
[2] Husslein T., I., Newns D.M., Pattnaik P-C-, Singer J-M-,
onte Carlo vidence for
-wave Painng in the 2D Hubbard Model ai a van
preprint submitted to Phys. Rev. Lett.
[3] Hubbard J., Froc. Roy. Soc.
[4] Emery V., Phys. Rev. Lent. 58 (1987) 2794.
[si von der Linden W., Phys. Repts. 220 (1992)
[6] Imada M. et al., J. Phys. Soc. Jpn 58
[7] Sorella S. et ai., Lent. 8 (1989) 663.
[8] Monthoux P. and Pines D., Phys. ev. Lent 69 [9] Rossât.Mignod J. et al., hysica B 186-188 (1993) 1;
ason T.E. et ai., Phys. Rev. ent. 71 (1993) 19;
Dheong S-W. et al., Phys. Rev. Lent. 67 (1992) 1791.
