Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
QuantumMob`Q3mini`
WickLogarithmicNegativity  |  |
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| n×n grn anm | | ||||
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Details and Options
Examples
(2)
Basic Examples
(1)
Set the number of fermion modes to consider.
In[1]:=
$n=6;
Construct a Wick state. Make sure that the state is normalized.
In[2]:=
SeedRandom[370];
In[3]:=
ws=RandomWickState[$n]
Out[3]=
WickState
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In[4]:=
Norm[ws]
Out[4]=
1
Consider a subsystem.
In[5]:=
aa=Range[$n/2]
Out[5]=
{1,2,3}
In[6]:=
neg=WickLogarithmicNegativity[ws,aa]//Chop
Out[6]=
2.35427+2.26618
For non-interacting fermions, the Green's function has sufficient information about the many-body state.
In[7]:=
grn=WickGreenFunction[ws]grn//ArrayShort
Out[7]=
NambuGreen
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Out[7]=
,
0.5101 | 0.0963945-0.180924 | -0.0509206-0.00607804 | -0.0210109+0.0714722 | … |
0.0963945+0.180924 | 0.637629 | 0.000330924+0.0620879 | 0.116681+0.210887 | … |
-0.0509206+0.00607804 | 0.000330924-0.0620879 | 0.224124 | 0.140732+0.156324 | … |
-0.0210109-0.0714722 | 0.116681-0.210887 | 0.140732-0.156324 | 0.43404 | … |
… | … | … | … | … |
0 | 0.024597-0.0378415 | -0.215658+0.0315273 | -0.0164584+0.0774082 | … |
-0.024597+0.0378415 | 0 | 0.117709+0.0304277 | 0.129995-0.089784 | … |
0.215658-0.0315273 | -0.117709-0.0304277 | 0 | -0.0898702-0.0229223 | … |
0.0164584-0.0774082 | -0.129995+0.089784 | 0.0898702+0.0229223 | 0 | … |
… | … | … | … | … |
Calculate the same mutual information from the Green's function.
In[8]:=
alt=WickLogarithmicNegativity[grn,aa]//Chop
Out[8]=
2.35427+2.26618
In[9]:=
neg-alt//Chop
Out[9]=
0
Scope
(1)
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""