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1
Lagrangian
2
E1
2.1
dispersion relation
2.1.1
heavy mass
3
E2
3.1
Plot
3.1.1
residual plot
3.2
Weight shift
3.2.1
Residual plot Ws
3.3
Compare the two methods for E2
3.4
E2 CM
3.4.1
To plot the figure in pdf
3.5
E2 Plateaux scan
3.5.1
E2_0_p1
3.5.2
E2_0_p111
3.6
E2_01
4
E2 connected
4.0.1
FT
ϕ
2
ϕ
2
4.0.2
Test ensemble
5
E3
5.1
Plot
5.1.1
residual plot
5.2
vev of
ϕ
2
ϕ
2
5.2.1
residual plot
5.3
Compare E3 fit
5.3.1
plotting the exponential for A1
5.3.2
plotting the exponential for p=(1,0,0)
5.4
E3 CM
5.5
E3 Plateaux scan
5.5.1
E3_0_A1
6
Matrix element
6.1
time ordering 1
6.1.1
T48
6.1.2
T32
6.2
time ordering 2
6.2.1
Fittint the contribution 1,4,5
6.3
free theory , time ordering 1
7
test area
7.0.1
g=0 {g=0 plot_GEVP tmp}
8
report fit
m
0
m
0
9
fit
a
00
a
00
10
report fit phase shift
δ
δ
10.0.1
Lattice dispersion relation
10.1
2 parameter fit
10.1.1
Continuum
10.1.2
Latt
E
−
E
f
r
e
e
−
l
a
t
t
+
E
f
r
e
e
−
c
o
n
t
E
−
E
f
r
e
e
−
l
a
t
t
+
E
f
r
e
e
−
c
o
n
t
10.1.3
Latt
E
C
M
E
C
M
with disp rel
10.1.4
to generate the pdf plot
11
Fit of the energy levels
11.1
P = (0,0,0), (1,0,0), (1,1,0)
11.2
P = (0,0,0), (1,0,0), (1,1,0) , (0,0,0)
11.3
P = (0,0,0), (1,0,0), (1,1,0) , (0,0,0) ,(1,1,1)
11.4
3 parameters fit
11.5
Lattice dispersion relation
12
Fit QC3
12.1
p=(0,0,0)
12.1.1
lattice dispersion relation
12.2
p=(1,0,0)
12.2.1
lattice dispersion relation
12.3
p=(1,1,0)
12.3.1
lattice dispersion relation p=(1,1,0)
12.4
p=(1-1,0,0)
12.4.1
latt disp rel
12.5
p=(1,1,1)
12.5.1
latt disp rel
12.6
tests
13
Polynomial fit E3
14
E
ϕ
1
E
ϕ
1
vs
E
3
ϕ
0
E
3
ϕ
0
14.0.1
P=(0,0,0)
14.0.2
P=(1,0,0)
14.0.3
P=(1,1,0)
15
E
ϕ
1
E
ϕ
1
-
E
3
ϕ
0
E
3
ϕ
0
16
m
0
=
−
4.89
m
0
=
−
4.89
16.1
E1
16.2
Heavy mass
17
g=0.025
17.1
E1 (g=0.025)
17.1.1
light mass
17.1.2
heavy mass
17.2
E2 (g=0.025)
17.2.1
residual plot
17.3
E2 CM
g
=
0.025
g
=
0.025
17.4
E3 (g=0.025)
17.4.1
residual plot
18
GEVP g0.025
18.1
P=(1,0,0)
19
GEVP g=0
19.1
current set GEVP g=0
19.2
old set
19.2.1
P=(0,0,0)
19.2.2
P=(1,0,0)
19.2.3
plotting the exponential
20
Fit 2 particle quantization (g=0.025)
21
Fit QC3 (g=0.025)
21.1
p=(0,0,0)
21.1.1
latt disp rel
21.2
p=(1,1,1)
21.2.1
latt disp rel
22
Smearing
22.1
Gaussian Smearing
22.2
Laplace smearing
23
GEVP g=0 m0=-4.9 m1=-4.68
23.1
GEVP P=(0,0,0)
23.2
GEVP P=(1,0,0) g0.25
23.2.1
../../g0.25/out/G2t_T64_L28_msq0-4.900000_msq1-4.650000_l02.500000_l12.500000_mu5.000000_g0.250000_rep0_output
24
g=0.25
24.1
derivative operator
24.2
operators
O
(
ϕ
0
,
ϕ
1
)
O
(
ϕ
0
,
ϕ
1
)
24.2.1
GEVP_phi0_phi03_phi1_v
24.2.2
GEVP_0_3_1_001_v
24.2.3
GEVP_0_3_1_001_011_v
24.2.4
GEVP_0_3_1_001_011_111_v
24.3
Hankel
24.4
phi3 non local
24.4.1
GEVP_phi0_phi03_phi1_v
24.4.2
GEVP_0_3_1_phi3nl_v
24.5
GEVP
ϕ
0
ϕ
0
ϕ
3
0
ϕ
0
3
ϕ
3
5
ϕ
5
3
24.6
GEVP
ϕ
0
ϕ
0
ϕ
3
0
ϕ
0
3
24.7
GEVP
ϕ
3
0
ϕ
0
3
ϕ
1
ϕ
1
24.8
GEVP
ϕ
0
ϕ
0
ϕ
1
ϕ
1
24.9
all L
m
2
0
=
−
4.868
m
0
2
=
−
4.868
m
2
1
=
−
4.71
m
1
2
=
−
4.71
24.10
m
2
0
=
−
4.868
m
0
2
=
−
4.868
m
2
1
=
−
4.70
m
1
2
=
−
4.70
24.11
m
2
0
=
−
4.868
m
0
2
=
−
4.868
m
2
1
=
−
4.72
m
1
2
=
−
4.72
24.12
m
2
0
=
−
4.9
m
0
2
=
−
4.9
m
2
1
=
−
4.68
m
1
2
=
−
4.68
24.13
m
2
0
=
−
4.868
m
0
2
=
−
4.868
m
2
1
=
−
4.68
m
1
2
=
−
4.68
24.14
m
2
0
=
−
4.868
m
0
2
=
−
4.868
m
2
1
=
−
4.67
m
1
2
=
−
4.67
24.15
m
2
0
=
−
4.868
m
0
2
=
−
4.868
m
2
1
=
−
4.65
m
1
2
=
−
4.65
24.16
λ
0
=
5
λ
0
=
5
24.17
neighbor interaction g
24.18
GEVP P=(1,0,0) g0.25
24.19
λ
=
0
λ
=
0
m
2
0
=
0.0489
m
0
2
=
0.0489
m
2
1
=
0.155
m
1
2
=
0.155
25
g=0.125
25.1
GEVP P=(0,0,0) g0.125
25.2
GEVP P=(1,0,0) g0.125
26
g=0.06
26.1
m
2
0
=
−
4.895
m
0
2
=
−
4.895
m
2
1
=
−
4.669
m
1
2
=
−
4.669
=
g
0.06
=
g
0.06
26.2
m
2
0
=
−
4.892
m
0
2
=
−
4.892
m
2
1
=
−
4.674
m
1
2
=
−
4.674
=
g
0.06
=
g
0.06
26.3
m
2
0
=
−
4.894
m
0
2
=
−
4.894
m
2
1
=
−
4.674
m
1
2
=
−
4.674
=
g
0.06
=
g
0.06
26.4
m
2
0
=
−
4.895
m
0
2
=
−
4.895
m
2
1
=
−
4.674
m
1
2
=
−
4.674
=
g
0.06
=
g
0.06
26.5
m
2
0
=
−
4.895
m
0
2
=
−
4.895
m
2
1
=
−
4.6745
m
1
2
=
−
4.6745
g
=
0.06
g
=
0.06
26.6
m
2
0
=
−
4.895
m
0
2
=
−
4.895
m
2
1
=
−
4.675
m
1
2
=
−
4.675
=
g
0.06
=
g
0.06
26.7
m
2
0
=
−
4.895
m
0
2
=
−
4.895
m
2
1
=
−
4.677
m
1
2
=
−
4.677
=
g
0.06
=
g
0.06
27
g=0.1
27.1
GEVP P=(0,0,0) g0.1
27.1.1
../../g0.1/out/G2t_T64_L28_msq0-4.900000_msq1-4.650000_l02.500000_l12.500000_mu5.000000_g0.100000_rep0_output
27.1.2
../../g0.1/out/G2t_T64_L26_msq0-4.900000_msq1-4.650000_l02.500000_l12.500000_mu5.000000_g0.100000_rep0_output
27.1.3
../../g0.1/out/G2t_T64_L36_msq0-4.900000_msq1-4.650000_l02.500000_l12.500000_mu5.000000_g0.100000_rep0_output
27.2
GEVP P=(1,0,0) g0.1
27.2.1
../../g0.1/out/G2t_T64_L26_msq0-4.900000_msq1-4.650000_l02.500000_l12.500000_mu5.000000_g0.100000_rep0_output
27.3
../../g0.1/out/G2t_T64_L28_msq0-4.900000_msq1-4.650000_l02.500000_l12.500000_mu5.000000_g0.100000_rep0_output
27.3.1
diff masses 2-1
27.4
../../g0.1/out/G2t_T64_L28_msq0-4.900000_msq1-4.650000_l02.500000_l12.500000_mu5.000000_g0.100000_rep0_output
27.5
t0=10 GEVP {t0_10_GEVP_g01}
27.5.1
../../g0.1/out/G2t_T64_L28_msq0-4.900000_msq1-4.650000_l02.500000_l12.500000_mu5.000000_g0.100000_rep0_output_GEVP10
27.6
m0=-4.893 GEVP {m0_4_893_GEVP_g01}
27.6.1
../../g0.1/out/G2t_T64_L28_msq0-4.893000_msq1-4.650000_l02.500000_l12.500000_mu5.000000_g0.100000_rep0_output
27.7
t0=t+3 GEVP
27.7.1
../../g0.1/out/G2t_T64_L28_msq0-4.900000_msq1-4.650000_l02.500000_l12.500000_mu5.000000_g0.100000_rep0_output
27.8
t=3 t0 variable GEVP
27.8.1
../../g0.1/out/G2t_T64_L28_msq0-4.900000_msq1-4.650000_l02.500000_l12.500000_mu5.000000_g0.100000_rep0_output
27.9
Gevp 4x4
27.9.1
../../g0.1/out/G2t_T64_L28_msq0-4.900000_msq1-4.650000_l02.500000_l12.500000_mu5.000000_g0.100000_rep0_output
27.9.2
../../g0.1/out/G2t_T64_L30_msq0-4.900000_msq1-4.650000_l02.500000_l12.500000_mu5.000000_g0.100000_rep0_output
27.9.3
../../g0.1/out/G2t_T64_L36_msq0-4.900000_msq1-4.650000_l02.500000_l12.500000_mu5.000000_g0.100000_rep0_output
27.10
GEVP P=(1,1,0) g0.1
27.10.1
../../g0.1/out/G2t_T64_L24_msq0-4.900000_msq1-4.650000_l02.500000_l12.500000_mu5.000000_g0.100000_rep0_output
27.11
GEVP g0.1 m0sq=-4.895 P=(1,0,0)
27.12
../../g0.1/out/G2t_T64_L36_msq0-4.895000_msq1-4.650000_l02.500000_l12.500000_mu5.000000_g0.100000_rep0_output
27.13
fit two particle sector
27.14
E2 CM g0.1
27.15
P = (0,0,0), (1,0,0), (1,1,0) g=0.1
27.16
P = (0,0,0), (1,0,0), (1,1,0) , (0,0,0) g=0.1
27.17
Lattice dispersion relation g=0.1
27.18
Polynomial fit E3 and E1_1 g0.1
27.19
fit QC3 pole g=0.1
28
normalised GEVP (GEVPn)
28.0.1
GEVP
28.0.2
GEVPn
References
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phi4-analysis
Chapter 6
Matrix element
In this chapter we report the test done to compute the matrix element
⟨
ϕ
1
|
ϕ
1
ϕ
3
0
|
3
ϕ
0
⟩
⟨
ϕ
1
|
ϕ
1
ϕ
0
3
|
3
ϕ
0
⟩