<s>
In	O
computational	O
solid	O
state	O
physics	O
,	O
Continuous-time	B-Algorithm
quantum	I-Algorithm
Monte	I-Algorithm
Carlo	I-Algorithm
(	O
CT-QMC	O
)	O
is	O
a	O
family	O
of	O
stochastic	O
algorithms	O
for	O
solving	O
the	O
Anderson	B-Algorithm
impurity	I-Algorithm
model	I-Algorithm
at	O
finite	O
temperature	O
.	O
</s>
<s>
These	O
methods	O
first	O
expand	O
the	O
full	O
partition	O
function	O
as	O
a	O
series	O
of	O
Feynman	O
diagrams	O
,	O
employ	O
Wick	O
's	O
theorem	O
to	O
group	O
diagrams	O
into	O
determinants	O
,	O
and	O
finally	O
use	O
Markov	B-General_Concept
chain	I-General_Concept
Monte	I-General_Concept
Carlo	I-General_Concept
to	O
stochastically	O
sum	O
up	O
the	O
resulting	O
series	O
.	O
</s>
<s>
The	O
attribute	O
continuous-time	O
was	O
introduced	O
to	O
distinguish	O
the	O
method	O
from	O
the	O
then-predominant	O
Hirsch	O
–	O
Fye	O
quantum	O
Monte	B-Algorithm
Carlo	I-Algorithm
method	I-Algorithm
,	O
which	O
relies	O
on	O
a	O
Suzuki	O
–	O
Trotter	O
discretisation	O
of	O
the	O
imaginary	O
time	O
axis	O
.	O
</s>
<s>
If	O
the	O
sign	O
problem	O
is	O
absent	O
,	O
the	O
method	O
can	O
also	O
be	O
used	O
to	O
solve	O
lattice	B-Algorithm
models	I-Algorithm
such	O
as	O
the	O
Hubbard	B-Algorithm
model	I-Algorithm
at	O
half	O
filling	O
.	O
</s>
<s>
To	O
distinguish	O
it	O
from	O
other	O
Monte	B-Algorithm
Carlo	I-Algorithm
methods	I-Algorithm
for	O
such	O
systems	O
that	O
also	O
work	O
in	O
continuous	O
time	O
,	O
the	O
method	O
is	O
then	O
usually	O
referred	O
to	O
as	O
Diagrammatic	O
determinantal	O
quantum	O
Monte	O
Carlo	O
(	O
DDQMC	O
or	O
DDMC	O
)	O
.	O
</s>
<s>
In	O
second	O
quantisation	O
,	O
the	O
Hamiltonian	O
of	O
the	O
Anderson	B-Algorithm
impurity	I-Algorithm
model	I-Algorithm
reads	O
:	O
</s>
<s>
In	O
a	O
final	O
step	O
,	O
one	O
notes	O
that	O
this	O
is	O
nothing	O
but	O
an	O
integral	O
over	O
a	O
large	O
domain	O
and	O
performs	O
it	O
using	O
a	O
Monte	B-Algorithm
Carlo	I-Algorithm
method	I-Algorithm
,	O
usually	O
the	O
Metropolis	B-Algorithm
–	I-Algorithm
Hastings	I-Algorithm
algorithm	I-Algorithm
.	O
</s>
