And we see how the non-cyc( '. 1 symmetric state ..... les. Let us denote by A1, A2 and
As the eigenvalues of T in decreasing size order. ",'. have
A e e- (- /4I -2/ 2 e-52/47" ) (4
A ) (4-
To/
A2 .e^/7 (4
27)
As 2 e-U/ + (e ,-- 2 + C--. (41
I..: energy levels are given -In Ak and we see that A2 is the one :ding to the
nor licly symmetric sector. From the simulation we will extract energy and we
have the unphysical one G, = In i'2 and the 1. I. 1 one C = In Unfortunately
the smaller gap is the uninteresting one and moreover, the unphysical gap goes to zero in
the small coupling limit because A, and A2 are degenerate. We shall see how the general
argument given above about the suppression of such v.. ,. 1 '. J relics works in this simple
case.
jure 4-7.
Energy levels of a typical TT. A schematic diagram showing the en.-
levels of a n--ical .... Ti levels are labelled for 1n- 0, 1, 2,... ordered
in ascending size within each sector, even and odd n labelling the cly
symmetric and asymmetric sectors respectively. Ti I.. ( ... level must
always be the lowest lying. We consider here the potentially troublesome
situation where EL < E2. 1-.: ordering of the remaining "r .- levels is
ort ant in the context of the current discussion.
Now let us consider an observable that can be calculated easily with the simulation.
Namely the average value of ':. at various sites given a fixed :: at (ij) = (1,1).
Let us denote by E,,, the sum over states n') = IT) and In') I= I) and let Z
)