<s>
Auxiliary-field	B-Algorithm
Monte	I-Algorithm
Carlo	I-Algorithm
is	O
a	O
method	O
that	O
allows	O
the	O
calculation	O
,	O
by	O
use	O
of	O
Monte	B-Algorithm
Carlo	I-Algorithm
techniques	I-Algorithm
,	O
of	O
averages	O
of	O
operators	O
in	O
many-body	B-Algorithm
quantum	O
mechanical	O
(	O
Blankenbecler	O
1981	O
,	O
Ceperley	O
1977	O
)	O
or	O
classical	O
problems	O
(	O
Baeurle	O
2004	O
,	O
Baeurle	O
2003	O
,	O
Baeurle	O
2002a	O
)	O
.	O
</s>
<s>
The	O
distinctive	O
ingredient	O
of	O
"	O
auxiliary-field	B-Algorithm
Monte	I-Algorithm
Carlo	I-Algorithm
"	O
is	O
the	O
fact	O
that	O
the	O
interactions	O
are	O
decoupled	O
by	O
means	O
of	O
the	O
application	O
of	O
the	O
Hubbard	B-Algorithm
–	I-Algorithm
Stratonovich	I-Algorithm
transformation	I-Algorithm
,	O
which	O
permits	O
the	O
reformulation	O
of	O
many-body	B-Algorithm
theory	I-Algorithm
in	O
terms	O
of	O
a	O
scalar	O
auxiliary-field	O
representation	O
.	O
</s>
<s>
This	O
reduces	O
the	O
many-body	B-Algorithm
problem	I-Algorithm
to	O
the	O
calculation	O
of	O
a	O
sum	O
or	O
integral	O
over	O
all	O
possible	O
auxiliary-field	O
configurations	O
.	O
</s>
<s>
In	O
this	O
sense	O
,	O
there	O
is	O
a	O
trade-off	O
:	O
instead	O
of	O
dealing	O
with	O
one	O
very	O
complicated	O
many-body	B-Algorithm
problem	I-Algorithm
,	O
one	O
faces	O
the	O
calculation	O
of	O
an	O
infinite	O
number	O
of	O
simple	O
external-field	O
problems	O
.	O
</s>
<s>
It	O
is	O
here	O
,	O
as	O
in	O
other	O
related	O
methods	O
,	O
that	O
Monte	O
Carlo	O
enters	O
the	O
game	O
in	O
the	O
guise	O
of	O
importance	B-Algorithm
sampling	I-Algorithm
:	O
the	O
large	O
sum	O
over	O
auxiliary-field	O
configurations	O
is	O
performed	O
by	O
sampling	O
over	O
the	O
most	O
important	O
ones	O
,	O
with	O
a	O
certain	O
probability	O
.	O
</s>
<s>
In	O
these	O
cases	O
,	O
one	O
has	O
to	O
resort	O
to	O
a	O
reweighting	O
procedure	O
(	O
i.e.	O
,	O
interpret	O
the	O
absolute	O
value	O
as	O
probability	O
and	O
multiply	O
the	O
sign	O
or	O
phase	O
to	O
the	O
observable	O
)	O
to	O
get	O
a	O
strictly	O
positive	O
reference	O
distribution	O
suitable	O
for	O
Monte	B-Algorithm
Carlo	I-Algorithm
sampling	I-Algorithm
.	O
</s>
<s>
However	O
,	O
it	O
is	O
well	O
known	O
that	O
,	O
in	O
specific	O
parameter	O
ranges	O
of	O
the	O
model	O
under	O
consideration	O
,	O
the	O
oscillatory	O
nature	O
of	O
the	O
weight	O
function	O
can	O
lead	O
to	O
a	O
bad	O
statistical	B-Algorithm
convergence	I-Algorithm
of	O
the	O
numerical	B-Algorithm
integration	I-Algorithm
procedure	O
.	O
</s>
<s>
The	O
problem	O
is	O
known	O
as	O
the	O
numerical	O
sign	O
problem	O
and	O
can	O
be	O
alleviated	O
with	O
analytical	O
and	O
numerical	O
convergence	B-Algorithm
acceleration	I-Algorithm
procedures	O
(	O
Baeurle	O
2002	O
,	O
Baeurle	O
2003a	O
)	O
.	O
</s>
