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Community-contributed installable additions to the Wolfram Language
QuantumMob`Q3mini`
NambuHermitian  |  |
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Details and Options
Examples
(2)
Basic Examples
(2)
Set the number of fermion modes to consider.
In[1]:=
$n=2;
Construct a BdG Hamiltonian matrix representing a BCS-type many-body Hamiltonian.
In[2]:=
SeedRandom[356];
In[3]:=
ham=RandomNambuHermitian[$n]ham//ArrayShort
Out[3]=
NambuHermitian
 |
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Out[3]=
,
-0.724099 | -0.834901-0.786713 |
-0.834901+0.786713 | -0.320198 |
0 | 0.609707-1.75869 |
-0.609707+1.75869 | 0 |
In[4]:=
mat=Matrix[ham]
Out[4]=
SparseArray
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Let us examine the above operator in a conventional form. To do it, choose a specific set of fermion modes.
In[1]:=
Let[Fermion,c]cc=c[Range@$n]ccc=Join[cc,Dagger@cc]
Out[1]=
{,}
c
1
c
2
Out[1]=
,,,
c
1
c
2
†
c
1
†
c
2
Manually construct a BCS-type Hamiltonian including pairing terms. Notice the factor of 1/2.
In[2]:=
alt=MultiplyDot[Dagger[ccc],Normal[ham].ccc]/2
Out[2]=
1
2
c
2
c
1
†
c
1
c
1
†
c
1
c
2
†
c
1
†
c
2
†
c
2
c
1
†
c
2
c
2
In[3]:=
new=Matrix[alt]
Out[3]=
SparseArray
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Compare the above single-particle Hamiltonian matrix with the original one.
In[4]:=
mat-new//ArrayZeroQ
Out[4]=
True
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""