Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
Wolfram`TensorNetworks`
MPSSchmidtValues  |
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Details and Options
Examples
(6)
Scope
(4)
Across all bonds
(1)
Sweep the Schmidt spectrum across every bond of an MPS to see how entanglement varies along the chain:
In[1]:=
mps=RandomTensorNetwork["MPS"[6,4,2]]
Out[2]=
TensorNetwork
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In[3]:=
(MPSSchmidtValues[mps,#1]&)/@Range[1,5]
Out[4]=
{{0.970888,0.239533},{0.963694,0.235972,0.123871,0.0163128},{0.91737,0.335568,0.189693,0.0992074},{0.714507,0.625619,0.296214,0.101676},{0.83564,0.549277}}
Maximally entangled cut
(1)
Product state
(1)
Canonicalization invariance
(1)
Applications
(1)
Properties & Relations
(1)
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Build a random matrix product state and pull the Schmidt values at a bond:
In[1]:=
mps=RandomTensorNetwork["MPS"[6,4,2]]
Out[1]=
TensorNetwork
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In[2]:=
MPSSchmidtValues[mps,3]
Out[2]=
{0.91737,0.335568,0.189693,0.0992074}
The squared values sum to one – the Schmidt coefficients are the square roots of a probability distribution:
In[3]:=
mps=RandomTensorNetwork["MPS"[6,4,2]];Total[MPSSchmidtValues[mps,3]^2]
Out[3]=
1.
Bond indices outside the valid range 1 through N-1 fall back to the trivial single-value distribution:
In[4]:=
mps=RandomTensorNetwork["MPS"[6,4,2]];{MPSSchmidtValues[mps,0],MPSSchmidtValues[mps,6]}
Out[4]=
{{1.},{1.}}
""