fPEPS

Fermionic projected entangled-pairs states and related algorithms. Abelian-symmetric tensor algebra is provided by Tensor.

What are projected entangled pair states

What are projected entangled pair states

• Basic concepts
  • Projected Entangled Pair States (PEPS)
  • Fermionic anticommutation rules in PEPS
  • Infinite PEPS (iPEPS)
  • Time evolution
  • Neighborhood tensor update (NTU)
  • Corner transfer matrix renormalization group (CTMRG)
  • Purification
  • References & Related Works

API: yastn.tn.fpeps

API: yastn.tn.fpeps

• Lattice Geometry
  • Basic Elements
  • Core Classes
• Creating PEPS
  • Initializing empty PEPS
  • Initializing product PEPS
  • Import and export PEPS
  • Double-layer PEPS
  • Double PEPS Tensor
• Time evolution
  • Evolution step
  • Gates
  • Predefined gates
  • Custom gates
• Environment NTU
  • Neighborhood tensor update environments
  • Approximate cluster update
• Environment CTM
  • The CTMRG iteration
  • Subspace-iteration mode
  • API
• CTM options
  • Two ways to pass them
  • Unknown options are rejected
  • From a configuration file, with command-line overrides
  • Reference
• Exact n-site measurement with opt_einsum
  • EnvCTM.measure_nsite_exact_oe()
  • EnvCTM.measure_nsite_norm_exact_oe()
  • EnvCTM.measure_nsite_numerator_exact_oe()
  • Network layout, bond labels and unrolling
  • Plain charged operators
  • Operators as MPO tensors
• Fixed-point CTMRG with implicit differentiation
  • Forward pass
  • Backward pass
  • Forward options carry over to the backward
  • Running on several devices: single-node multi-gpu
  • C4v-symmetric variant
  • Example
  • API
• Environment BoundaryMPS
  • EnvBoundaryMPS
• Environment BP
  • Belief propagation environments

Examples: basics of usage

Examples: basics of usage

• Lattice geometry
• CTMRG for 2D Ising model
• 2D Fermi-Hubbard model at finite temperature
• Kibble-Zurek quench in 2D transverse-field Ising model