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MPS

Matrix product state.

MPS 

MPS(
    tensors: List[Tensor],
    bc: str = "OBC",
    center: Optional[int] = None,
    itag_prefix: Optional[str] = None,
)

Bases: Network

Matrix product state.

Each site tensor has axes (left_bond, right_bond, physical) where the physical axis at site i carries itag s{i:02d}.

Parameters:

Name Type Description Default
tensors List[Tensor]

List of site tensors, each with exactly 3 axes (left_bond, right_bond, physical). The physical axis at site i must carry itag s{i:02d}.

 required
bc str

Boundary condition: 'OBC' (default) or 'PBC'.

 'OBC'
center Optional[int]

Orthogonality center site index, or None if unspecified.

 None
itag_prefix Optional[str]

Bond itag prefix string. Defaults to 'A' when None.

 None

Raises:

Type Description
ValueError

If any tensor has the wrong number of axes, an incorrect physical itag, or adjacent bond indices are inconsistent.

String Representation

repr(mps) (and therefore the interactive display in notebooks and REPLs) renders a text diagram of the chain:

                 Matrix Product State (MPS)                 
                 ‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾                 
           ○───○───○───○─···─⊙─···─○───○───○───○            
           ╵   ╵   ╵   ╵     ╵     ╵   ╵   ╵   ╵            
               length: 100     max bond: 64
               center: 49      norm: 1.00e+00

Chain row — each node is one site; consecutive sites are joined by ───. When the chain is too long to show in full, a gap ─···─ is inserted and only a subset of sites near the edges and center is displayed.

Physical-index row — the downward stub ╵ beneath each node represents the physical index of that site.

Node symbols:

Symbol Meaning
○ Regular site
⊙ Orthogonality center (center attribute)

Info block — length is the number of sites L; max bond is the largest bond dimension across all virtual indices; center is the orthogonality center index (None if not set); norm is ‖ψ‖.

See Also

  • Network — base class providing canonical(), norm(), serialize(), and more.
  • MPO — matrix product operator.
  • observe — compute ⟨ψ|O|ψ⟩ for an MPS state.
  • dmrg.run — optimize an MPS with DMRG.