<s>
In	O
solid-state	O
physics	O
,	O
the	O
t-J	B-Algorithm
model	I-Algorithm
is	O
a	O
model	O
first	O
derived	O
in	O
1977	O
from	O
the	O
Hubbard	B-Algorithm
model	I-Algorithm
by	O
Józef	O
Spałek	O
to	O
explain	O
antiferromagnetic	O
properties	O
of	O
the	O
Mott	O
insulators	O
and	O
taking	O
into	O
account	O
experimental	O
results	O
about	O
the	O
strength	O
of	O
electron-electron	O
repulsion	O
in	O
this	O
materials	O
.	O
</s>
<s>
The	O
model	O
consider	O
the	O
materials	O
as	O
a	O
lattice	B-Algorithm
with	O
atoms	O
in	O
the	O
knots	O
(	O
sites	O
)	O
and	O
just	O
one	O
or	O
two	O
external	O
electrons	O
moving	O
among	O
them	O
(	O
internal	O
electrons	O
are	O
not	O
considered	O
)	O
,	O
like	O
in	O
the	O
basic	O
Hubbard	B-Algorithm
model	I-Algorithm
.	O
</s>
<s>
That	O
difference	O
is	O
in	O
supposing	O
electrons	O
being	O
strongly-correlated	O
,	O
that	O
means	O
electrons	O
are	O
very	O
sensible	O
to	O
reciprocal	O
coulombic	O
repulsion	O
,	O
and	O
so	O
are	O
more	O
constrained	O
to	O
avoid	O
occupying	O
lattice	B-Algorithm
's	O
sites	O
already	O
occupied	O
by	O
another	O
electron	O
.	O
</s>
<s>
In	O
the	O
basic	O
Hubbard	B-Algorithm
model	I-Algorithm
,	O
the	O
repulsion	O
,	O
indicated	O
with	O
U	O
,	O
can	O
be	O
small	O
and	O
also	O
null	O
,	O
and	O
electrons	O
are	O
freer	O
to	O
jump	O
(	O
hopping	O
,	O
parametrized	O
by	O
t	O
as	O
transfer	O
or	O
tunnel	O
)	O
from	O
one	O
site	O
to	O
another	O
.	O
</s>
<s>
In	O
the	O
t-J	B-Algorithm
model	I-Algorithm
,	O
instead	O
of	O
U	O
,	O
there	O
is	O
the	O
parameter	O
J	O
,	O
function	O
of	O
the	O
ratio	O
t/U	O
,	O
so	O
the	O
name	O
.	O
</s>
<s>
It	O
is	O
used	O
as	O
a	O
possible	O
model	O
to	O
explain	O
high	O
temperature	O
superconductivity	O
in	O
doped	B-Algorithm
antiferromagnets	O
,	O
in	O
the	O
hypothesis	O
of	O
strong	O
coupling	O
between	O
electrons	O
.	O
</s>
<s>
The	O
t-J	O
Hamiltonian	O
can	O
be	O
derived	O
from	O
the	O
of	O
the	O
Hubbard	B-Algorithm
model	I-Algorithm
using	O
the	O
Schrieffer	O
–	O
Wolff	O
transformation	O
,	O
with	O
the	O
transformation	O
generator	O
depending	O
on	O
t/U	O
and	O
excluding	O
the	O
possibility	O
for	O
electrons	O
to	O
doubly	O
occupy	O
a	O
lattice	B-Algorithm
's	O
site	O
,	O
which	O
results	O
in	O
:	O
</s>
<s>
where	O
the	O
term	O
in	O
t	O
corresponds	O
to	O
the	O
kinetic	O
energy	O
and	O
is	O
equal	O
to	O
the	O
one	O
in	O
the	O
Hubbard	B-Algorithm
model	I-Algorithm
.	O
</s>
<s>
The	O
second	O
one	O
is	O
the	O
potential	O
energy	O
approximated	O
at	O
the	O
second	O
order	O
,	O
because	O
this	O
is	O
an	O
approximation	O
of	O
the	O
Hubbard	B-Algorithm
model	I-Algorithm
in	O
the	O
limit	O
U	O
>>	O
t	O
developed	O
in	O
power	O
of	O
t	O
.	O
Terms	O
at	O
higher	O
order	O
can	O
be	O
added	O
.	O
</s>
<s>
is	O
the	O
sum	O
over	O
nearest-neighbor	O
sites	O
i	O
and	O
j	O
,	O
for	O
all	O
sites	O
,	O
typically	O
on	O
a	O
two-dimensional	O
square	O
lattice	B-Algorithm
,	O
</s>
<s>
σ	O
is	O
the	O
spin	B-General_Concept
polarization	I-General_Concept
,	O
</s>
<s>
J	O
is	O
the	O
antiferromagnetic	O
exchange	B-General_Concept
coupling	I-General_Concept
,	O
J	O
=	O
,	O
</s>
<s>
ni	O
=	O
cc	O
is	O
the	O
particle	O
number	O
at	O
site	O
i	O
and	O
can	O
be	O
maximum	O
1	O
,	O
so	O
that	O
double	O
occupancy	O
is	O
forbidden	O
(	O
in	O
the	O
Hubbard	B-Algorithm
model	I-Algorithm
is	O
possible	O
)	O
,	O
</s>
<s>
If	O
ni	O
=	O
1	O
,	O
that	O
is	O
when	O
in	O
the	O
ground	O
state	O
,	O
there	O
is	O
just	O
one	O
electron	O
per	O
lattice	B-Algorithm
's	O
site	O
(	O
half-filling	O
)	O
,	O
the	O
model	O
reduces	O
to	O
the	O
Heisenberg	O
model	O
and	O
the	O
ground	O
state	O
reproduce	O
a	O
dielectric	O
antiferromagnets	O
(	O
Mott	O
insulator	O
)	O
.	O
</s>
