Environment BoundaryMPS#
Boundary MPS approach for contracting finite lattice. It supports expectation values, including long-range correlations, sampling, etc.
- class yastn.tn.fpeps.EnvBoundaryMPS(psi, opts_svd, setup='l', opts_var=None)[source]#
Boundary MPS class for finite PEPS contraction.
A PEPS instance on a specified lattice can be initialized as empty (with no tensors assiged) or with tensors assigned to each unique lattice site.
PEPS inherits key methods (e.g., sites, bonds, dims) from the associated lattice geometry. Supports
[]notation to get/set individual tensors. PEPS tensors can be either rank-5 (including physical legs) or rank-4 (without physical legs). Leg enumeration follows the order: top, left, bottom, right, and physical leg.- Parameters:
geometry (SquareLattice | CheckerboardLattice | RectangularUnitcell) – Specify lattice geometry.
tensors (Optional[Sequence[Sequence[Tensor]] | dict[tuple[int,int],Tensor]]]) – Fill in the Peps lattice with tensors. Each unique sites should get assigned in a way consistent with the geometry.
Example
import yastn import yastn.tn.fpeps as fpeps # PEPS with CheckerboarLattice geometry and no tensors assigned. # geometry = fpeps.CheckerboardLattice() psi = fpeps.Peps(geometry) config = yastn.make_config(sym='U1') leg = yastn.Leg(config, s=1, t=(0, 1), D=(1, 1)) # # for rank-5 tensors # A00 = yastn.rand(config, legs=[leg.conj(), leg, leg, leg.conj(), leg]) psi[0, 0] = A00 # # Currently, 5-leg PEPS tensors are fused by __setitem__ as ((top-left)(bottom-right) physical). # This is done to work with objects having a smaller number of blocks. assert psi[0, 0].ndim == 3 assert (psi[0, 0].unfuse_legs(axes=(0, 1)) - A00).norm() < 1e-13 # PEPS with no physical legs is also possible. # # for rank-4 tensors # B00 = yastn.rand(config, legs=[leg.conj(), leg, leg, leg.conj()]) psi[0, 0] = B00 assert psi[0, 0].ndim == 4 # PEPS with tensors assigned during initialization # psi = fpeps.Peps(geometry, tensors={(0, 0): A00, (0, 1): A01}) # # or equivalently # psi = fpeps.Peps(geometry, tensors=[[A00, A01], [A01, A00]]) # above, some provided tensors are redundant, although this redundancy is consistent with the geometry.
- measure_1site(O)[source]#
Calculate all 1-point expectation values <O_j> in a finite PEPS.
Takes CTM environments and operators.
- Parameters:
O (dict[tuple[int, int], dict[int, operators]]) – mapping sites with list of operators at each site.
- measure_2site(O, P, opts_svd, opts_var=None)[source]#
Calculate all 2-point correlations <O_i P_j> in a finite PEPS.
Takes CTM environments and operators.
- Parameters:
O, P (dict[tuple[int, int], dict[int, operators]],) – mapping sites with list of operators at each site.