Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
QuantumMob`Q3mini`
WickEntanglementEntropy  |  |
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Details and Options
Examples
(1)
Basic Examples
(1)
Set the number of fermion modes to consider.
In[1]:=
$n=6;
Construct a Wick state. Make sure that it is normalized because many functions such as and expect a normalized state as input.
In[2]:=
SeedRandom[347];
In[3]:=
ws=RandomWickState[$n]
Out[3]=
WickState
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In[4]:=
Norm[ws]
Out[4]=
1
Take the half of the system as one subsystem.
In[5]:=
aa=Range[$n/2]
Out[5]=
{1,2,3}
Calculate the entanglement entropy.
In[6]:=
ent=WickEntanglementEntropy[ws,aa]
Out[6]=
1.8867
You can also calculate the entanglement entropy using the Green's function.
In[7]:=
gg=WickGreenFunction[ws]//Chop;gg//ArrayShort
Out[7]=
,
0.301477 | 0.0656129+0.0235416 | -0.147069+0.00887366 | 0.0479388-0.128885 | … |
0.0656129-0.0235416 | 0.353766 | 0.0535252+0.0640552 | 0.082095+0.0898905 | … |
-0.147069-0.00887366 | 0.0535252-0.0640552 | 0.470892 | -0.100396+0.0200553 | … |
0.0479388+0.128885 | 0.082095-0.0898905 | -0.100396-0.0200553 | 0.477254 | … |
… | … | … | … | … |
0 | -0.0265307+0.140911 | -0.126166+0.00947692 | -0.116034-0.0215489 | … |
0.0265307-0.140911 | 0 | -0.250196-0.0528364 | 0.111321+0.153215 | … |
0.126166-0.00947692 | 0.250196+0.0528364 | 0 | 0.204128-0.156129 | … |
0.116034+0.0215489 | -0.111321-0.153215 | -0.204128+0.156129 | 0 | … |
… | … | … | … | … |
In[8]:=
new=WickEntanglementEntropy[gg,aa]
Out[8]=
1.8867
In[9]:=
ent-new//Chop
Out[9]=
0
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