the ground state of the simulation in the previous run. Since, in practice, we often ran
simulations with similar coupling right after the other, so this should be a very safe end
accurate standard.
4.2.3 Comparison of small M results: Exact Numerical vs. Monte Carlo
Let us first look at the simplest of cases, namely the M = 2 case. This can be solved
exactly with arbitrary N. At every time-slice we have a 3 state system corresponding to
SIT), I T) and I| T). Recall that the [{) state is not allowed on a periodic lattice. In this
ordered basis the transfer matrix is
/ e-p /4To 0 e-5p2/s8T
as can be read off from the rules 4-3).
to make 72 hermitian. It is illustrative
V21o
e- 2/4To 9 g 5p-/8To (4-2
__ / To
) 5p2/8TO p-2/IO
,/5% e /
The off-diagonal elements have been symmetrized
to use the basis:
1
I-) (I IT)- I ))
v2
1
2+) (I I T) + I Ti))
|2) i|T )
where the transfer matrix becomes
e-2 /4To
T 0
0
0
e-p /4To
0 e-5p2/s8T
TO
0
_kg-5p /8To
To
e-'/rTo
1)
(4 22)
(4-23)
(4-24)
(4-25)