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Community-contributed installable additions to the Wolfram Language
Wolfram`TensorNetworks`
MPSCanonicalForm  |
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The MPS routines assume the open-boundary tensor layout used by ["MPS"]: bulk tensors with shape {leftBond, rightBond, physical}, and boundary tensors at sites 1 and with shape {bond, physical}.
n
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Left-canonical form makes every tensor satisfy .A=I when the bulk tensor is reshaped as a (leftBond × physical) × rightBond matrix; right-canonical form gives when reshaped as leftBond × (rightBond × physical).
[i]
A
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A
A.=I
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Mixed canonical form left-canonicalizes sites 1 through and right-canonicalizes sites through , leaving site as the orthogonality center carrying the full spectral weight. This is the standard form for measurement on site and for DMRG-style local updates.
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k+1
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Canonicalization proceeds by sweeping from one boundary to the other; with every bond is capped at dimension , and with singular values not exceeding are dropped.
"MaxBond"D
D
"Tolerance"ϵ
ϵ
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Without truncation options the result represents the same network as the input up to a gauge transformation; between the input and its canonical form equals [mps][canon].
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The following options can be given:
"MaxBond"  | maximum bond dimension retained after SVD truncation | ||
"Tolerance" | 0 | singular-value cutoff; values not exceeding this are dropped |
Examples
(11)
Basic Examples
(4)
Build a six-site MPS with bond dimension 4 and physical dimension 2, then transform it to canonical form. With no form argument MPSCanonicalForm defaults to left-canonical:
In[1]:=
mps=BlockRandomSeedRandom[42];
["MPS"[6,4,2]]
 | RandomTensorNetwork |
Out[1]=
TensorNetwork
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In[2]:=
 | MPSCanonicalForm |
Out[2]=
TensorNetwork
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Transform to right-canonical form:
In[1]:=
mps=BlockRandomSeedRandom[42];
["MPS"[6,4,2]];
[mps,"Right"]
 | RandomTensorNetwork |
| MPSCanonicalForm |
Out[1]=
TensorNetwork
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Mixed canonical form centered at site 3 – sites 1 and 2 are left-isometric, sites 4 through 6 are right-isometric, and site 3 holds the wavefunction's spectral weight:
In[1]:=
mps=BlockRandomSeedRandom[42];
["MPS"[6,4,2]];
[mps,{"Mixed",3}]
| RandomTensorNetwork |
| MPSCanonicalForm |
Out[1]=
TensorNetwork
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The form argument is explicit. and return the same network:
In[1]:=
mps=BlockRandomSeedRandom[42];
["MPS"[6,4,2]];
[mps,"Left"]
| RandomTensorNetwork |
| MPSCanonicalForm |
Out[1]=
TensorNetwork
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Scope
(2)
Options
(2)
Applications
(2)
Properties & Relations
(1)
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