Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
QuantumMob`Q3mini`
Spin  |
Details and Options
Examples
(6)
Basic Examples
(4)
In[1]:=
Let[Spin,J]
In[2]:=
Dagger[J[1,3]]Dagger[J[1,3]]//TeXForm
Out[2]=
Z
J
1
Out[2]//TeXForm=
J_1^{ ext{Z}}
In[3]:=
J[1,1]**J[1,1]**J[2]J[1,2]**(J[1,2]**J[1,3])J[3]**J[3]**J[1,3]
Out[3]=
Y
J
4
Out[3]=
Z
J
1
4
Out[3]=
Z
J
1
4
In[4]:=
J[1,4]
Out[4]=
+
J
1
In[5]:=
J[1,6]
Out[5]=
H
J
1
In[6]:=
J[a,3]
Out[6]=
Z
J
a
Consider the computation basis for a two-spin system.
In[7]:=
bs=Basis[J@{1,2}]
Out[7]=
,,,
1
2
J
1
1
2
J
2
1
2
J
1
-
1
2
J
2
-
1
2
J
1
1
2
J
2
-
1
2
J
1
-
1
2
J
2
In[8]:=
J[1,4]**bsJ[1,5]**bs
Out[8]=
0,0,,
1
2
J
1
1
2
J
2
1
2
J
1
-
1
2
J
2
Out[8]=
,,0,0
-
1
2
J
1
1
2
J
2
-
1
2
J
1
-
1
2
J
2
In[9]:=
J[3,4]**bsJ[3,5]**bs
Out[9]=
{0,0,0,0}
Out[9]=
,,,
1
2
J
1
1
2
J
2
-
1
2
J
3
1
2
J
1
-
1
2
J
2
-
1
2
J
3
-
1
2
J
1
1
2
J
2
-
1
2
J
3
-
1
2
J
1
-
1
2
J
2
-
1
2
J
3
In[10]:=
J[1,1]**bsJ[1,2]**bsJ[1,3]**bs
Out[10]=
,,,
1
2
-
1
2
J
1
1
2
J
2
1
2
-
1
2
J
1
-
1
2
J
2
1
2
1
2
J
1
1
2
J
2
1
2
1
2
J
1
-
1
2
J
2
Out[10]=
,,-,-
1
2
-
1
2
J
1
1
2
J
2
1
2
-
1
2
J
1
-
1
2
J
2
1
2
1
2
J
1
1
2
J
2
1
2
1
2
J
1
-
1
2
J
2
Out[10]=
,,-,-
1
2
1
2
J
1
1
2
J
2
1
2
1
2
J
1
-
1
2
J
2
1
2
-
1
2
J
1
1
2
J
2
1
2
-
1
2
J
1
-
1
2
J
2
In[1]:=
Let[Spin,J,Spin1]
In[2]:=
J[1,2]**J[1,0]**J[1,2]**J[1,0]**J[1,0]
Out[2]=
Y
J
1
Y
J
1
In[3]:=
J[a,1]**J[1,2]**J[1,0]**J[1,2]**J[1,0]**J[1,0]
Out[3]=
Y
J
1
Y
J
1
X
J
a
In[4]:=
J[1,0]**J[1,0]**J[1,0]**J[1,0]**J[1,0]
Out[4]=
0
J
1
In[1]:=
Let[Spin,S,Spin2]
In[2]:=
S[2]
Out[2]=
Y
S
In[3]:=
S^2**S^2
Out[3]=
SSSS
In[4]:=
J[3]**J[1]**J[2]
Out[4]=
-++
X
J
X
J
Y
J
Y
J
X
J
Y
J
Z
J
In[5]:=
J[1,1]**J[2,1]+J[1,2]**J[2,2]+J[1,3]**J[2,3]
Out[5]=
X
J
1
X
J
2
Y
J
1
Y
J
2
Z
J
1
Z
J
2
In[6]:=
MultiplyDot[J[1,All],J[2,All]]
Out[6]=
X
J
1
X
J
2
Y
J
1
Y
J
2
Z
J
1
Z
J
2
In[7]:=
J[4,4]//TeXForm
Out[7]//TeXForm=
J_4^+
In[8]:=
J[1,0]**J[1,1,2]**J[2,3]**J[1]**J[2,3]**J[1,2,1]
Out[8]=
X
J
0
J
1
Z
J
2
Z
J
2
Y
J
1,1
X
J
1,2
In[1]:=
Let[Fermion,c,Vacuum"Sea"]Let[Fermion,d]Let[Fermion,f,Spin0,Vacuum"Sea"]
In[2]:=
Spin[c]
Out[2]=
1
2
For an operator with non-zero spin, the last flavor index should be consistent with the proper spin component. In the example below, the flavor index was not consistent and hence the spin is regarded as zero:
In[3]:=
Spin[c[1]]Spin[Dagger[c[1]]]
Out[3]=
0
Out[3]=
0
Compare the above example with the one below.
In[4]:=
Spin[c[1,1/2]]
Out[4]=
1
2
Therefore, while this is legitimate
In[5]:=
FockSpin[c[1]]
Out[5]=
+,-,-+
1
2
†
c
1,↓
c
1,↑
1
2
†
c
1,↑
c
1,↓
1
2
†
c
1,↓
c
1,↑
1
2
†
c
1,↑
c
1,↓
1
2
†
c
1,↓
c
1,↓
1
2
†
c
1,↑
c
1,↑
the following is problematic
You can see why by the following examples.
Sometimes one may not care about the precise spin. Then you can turn off the message.
Of course, you can turn it on again whenever you want.