MPS

Abelian-symmetric matrix product states/operators and related algorithms. Abelian-symmetric tensor algebra is provided by YASTN.

An implementation of Matrix Product State (Mps) and Matrix Product Operator (Mpo) employing yastn.Tensor.

What are matrix product states

What are matrix product states

• Basic concepts
  • Matrix product state (MPS)
  • Matrix product operator (MPO)
  • Canonical form
  • Algorithms
  • Measurements
  • References

API: yastn.tn.mps

API: yastn.tn.mps

• Creating MPS and MPO
  • Initializing empty MPS/MPO
  • Setting MPS/MPO tensors by hand
  • Initializing product MPS/MPO
  • Initializing random MPS/MPO
  • Generating MPO using Hterm
  • Generator class for MPO/MPS (beta)
  • Making a copy of MPS/MPO
  • Import and export MPS/MPO from/to different formats
• Properties
  • Geometry
  • Symmetry
  • Index convention
  • Physical and virtual spaces
• Expectation values
  • Overlaps and MPO expectation values
  • Shorthand notation
  • One- and two-point expectation values
  • Schmidt values and entropy profile
  • Sampling
• Algebra
  • Multiplication by a scalar
  • Conjugation and transpose
  • Addition of MPS/MPO
  • Products of MPO and MPS
  • Multiplication with truncation
• Canonizing MPS/MPO
  • MpsMpoOBC.canonize_()
  • MpsMpoOBC.truncate_()
  • MpsMpoOBC.orthogonalize_site_()
  • MpsMpoOBC.absorb_central_()
  • MpsMpoOBC.diagonalize_central_()
• Density matrix renormalization group (DMRG)
  • dmrg_()
  • Single-site DMRG
  • Two-site DMRG
  • Projecting out selected MPS
  • Auxilliary mutable Method class
• Time-dependent variational principle (TDVP)
  • tdvp_()
• Variational overlap maximization
  • compression_()
• Environments
  • Env()
  • on_bra()
  • Environment classes

Examples: basics of usage

Examples: basics of usage

• Initialization and creation operations
  • Building MPS/MPO manually
  • Building MPO using Hterm
  • Generator class for MPO/MPS
  • Save and load MPS/MPO
• Expectation values
  • Expectation values in AKLT state
  • Entropy and spectrum in GHZ-like state
• Algebra
  • Canonical form by QR
  • Canonical form by SVD
  • Multiplication
• Algorithms: DMRG
  • Low energy states of the XX model
• Algorithms: TDVP
  • Sudden quench in a free-fermionic model
  • Quench across a quantum critical point in a transverse Ising chain