Environment NTU#

Neighborhood tensor update environments#

class yastn.tn.fpeps.EnvNTU(psi, which='NN')[source]#

Supports a family of NTU environments for truncation of PEPS tensors during time evolution. The local exact contractions, and SVD-1 approximation used in some environments, preserve hermiticity and positivity of the metric tensor. Numerical noise breaking those properties can still appear and grow with the number of environment layers.

Parameters:

  • psi (yastn.tn.Peps) – Peps state being evolved.

  • which (str) – Type of environment from ‘NN’, ‘NN+’, ‘NN++’, ‘NNN’, ‘NNN+’, ‘NNN++’

bond_metric(Q0, Q1, s0, s1, dirn)[source]#

Calculate bond metric. The environment size is controlled by which.

Below, double lines indicate core bonds that are contracted exactly. Dashed lines indicate tree-like approximations, where border tensors are approximated using SVD-1, i.e., product boundary vectors from a rank-one SVD decomposition. Such approximation preserves positivity of the calculated metric.

If which == 'NN':

          (-1 +0)══(-1 +1)
             ║        ║
   (+0 -1)═══Q0══   ══Q1═══(+0 +2)
             ║        ║
          (+1 +0)══(+1 +1)


If which == 'NN+':

                (-2 +0)┈┈(-2 +1)
                   ┊        ┊
        (-1 -1)┄(-1 +0)══(-1 +1)┄(-1 +2)
           ┊       ║        ║       ┆
(+0 -2)═(+0 -1)════Q0══   ══Q1═══(+0 +2)═(+0 +3)
           ┊       ║        ║       ┆
        (+1 -1)┄(+1 +0)══(+1 +1)┄(+1 +2)
                   ┊        ┊
                (+2 +0)┈┈(+2 +1)


If which == 'NN++':

                        (-3 +0)┈┈(-3 +1)
                           ┊        ┊
                (-2 -1)┈(-2 +0)┈┈(-2 +1)┈(-2 +2)
                   ┊       ┊        ┊       ┊
        (-1 -2)┈(-1 -1)┈(-1 +0)══(-1 +1)┈(-1 +2)┈(-1 +3)
           ┊       ┊       ║        ║       ┊       ┊
(+0 -3)═(+0 -2)═(+0 -1)════Q0══   ══Q1═══(+0 +2)=(+0 +3)=(+0 +4)
           ┊       ┊       ║        ║       ┊       ┊
        (+1 -2)┈(+1 -1)┈(+1 +0)══(+1 +1)┈(+1 +2)┈(+1 +3)
                   ┊       ┊        ┊       ┊
                (+2 -1)┈(+2 +0)┈┈(+2 +1)┈(+2 +2)
                           ┊        ┊
                        (+3 +0)┈┈(+3 +1)


If which == 'NNN':

    (-1 -1)=(-1 +0)══(-1 +1)=(-1 +2)
       ║       ║        ║       ║
    (+0 -1)════Q0══   ══Q1═══(+0 +2)
       ║       ║        ║       ║
    (+1 -1)=(+1 +0)══(+1 +1)=(+1 +2)


If which == 'NNN+':

        (-2 -1) (-2 +0)  (-2 +1) (-2 +2)
           ║       ║        ║       ║
(-1 -2)=(-1 -1)=(-1 +0)══(-1 +1)=(-1 +2)=(-1 +3)
           ║       ║        ║       ║
(+0 -2)=(+0 -1)════Q0══   ══Q1═══(+0 +2)=(+0 +3)
           ║       ║        ║       ║
(+1 -2)=(+1 -1)=(+1 +0)══(+1 +1)=(+1 +2)=(+1 +3)
           ║       ║        ║       ║
        (+2 -1) (+2 +0)  (+2 +1) (+2 +2)


If which == 'NNN++':

        (-3 -2)┈(-3 -1)┈(-3 +0)┈┈(-3 +1)┈(-3 +2)┈(-3 +3)
            ┊      ┊       ┊        ┊       ┊       ┊
(-2 -3)┈(-2 -2)┈(-2 -1)┈(-2 +0)┈┈(-2 +1)┈(-2 +2)┈(-2 +3)┈(-2 +4)
   ┊        ┊      ┊       ┊        ┊       ┊       ┊       ┊
(-1 -3)┈(-1 -2)┈(-1 -1)=(-1 +0)══(-1 +1)=(-1 +2)┈(-1 +3)┈(-1 +4)
   ┊        ┊      ║       ║        ║       ║       ┊       ┊
(+0 -3)=(+0 -2)=(+0 -1)════Q0══   ══Q1═══(+0 +2)=(+0 +3)=(+0 +4)
   ┊        ┊      ║       ║        ║       ║       ┊       ┊
(+1 -3)┈(+1 -2)┈(+1 -1)=(+1 +0)══(+1 +1)=(+1 +2)┈(+1 +3)┈(+1 +4)
   ┊        ┊      ┊       ┊        ┊       ┊       ┊       ┊
(+2 -3)┈(+2 -2)┈(+2 -1)┈(+2 +0)┈┈(+2 +1)┈(+2 +2)┈(+2 +3)┈(+2 +4)
            ┊      ┊       ┊        ┊       ┊       ┊
        (+3 -2)┈(+3 -1)┈(+3 +0)┈┈(+3 +1)┈(+3 +2)┈(+3 +3)

Approximate cluster update#

class yastn.tn.fpeps.EnvApproximate(psi, which='65', opts_svd=None, opts_var=None, update_sweeps=None)[source]#

Supports calculation of bond metric for larger local clusters, which are contracted approximately using the boundary MPS approach.

Parameters:

  • psi (yastn.tn.Peps) – Peps state being evolved.

  • which (str) – Type of environment from ‘43’, ‘43+’, ‘65’, ‘65+’, ‘87’, ‘87+’

  • opts_svd (dict) – Passed to yastn.tn.mps.zipper() for truncation in boundary MPS calculation.

  • opts_var – Passed to yastn.tn.mps.compression_() for boundary MPS variational fine-tunning.

  • update_sweeps – Passed as max_sweeps to yastn.tn.mps.compression_() for boundary MPS variational fine-tunning.

bond_metric(Q0, Q1, s0, s1, dirn)[source]#

Calculates bond metric. The environment size is controlled by which.

Approximately contract the diagram using boundary MPS approach, parallel to the metric (open) bond direction.

If which == '65':

    (-2 -2)═(-2 -1)═(-2 +0)══(-2 +1)═(-2 +2)═(-2 +3)
       ║       ║       ║        ║        ║        ║
    (-1 -2)═(-1 -1)═(-1 +0)══(-1 +1)═(-1 +2)═(-1 +3)
       ║       ║       ║        ║        ║        ║
    (+0 -2)═(+0 -1)════Q0══   ══Q1═══(+0 +2)═(+0 +3)
       ║       ║       ║        ║        ║        ║
    (+1 -2)═(+1 -1)═(+1 +0)══(+1 +1)═(+1 +2)═(+1 +3)
       ║       ║       ║        ║        ║        ║
    (+2 -2)═(+2 -1)═(+2 +0)══(+2 +1)═(+2 +2)═(+2 +3)


If which == '65+':

            (-3 -2) (-3 -1) (-3 +0)  (-3 +1) (-3 +2)  (-3 +3)
               ║       ║       ║        ║       ║        ║
    (-2 -3)═(-2 -2)═(-2 -1)═(-2 +0)══(-2 +1)═(-2 +2)══(-2 +3)═(-2 +4)
               ║       ║       ║        ║       ║        ║
    (-1 -3)═(-1 -2)═(-1 -1)═(-1 +0)══(-1 +1)═(-1 +2)══(-1 +3)═(-1 +4)
               ║       ║       ║        ║       ║        ║
    (+0 -3)═(+0 -2)═(+0 -1)════Q0══   ══Q1═══(+0 +2)══(+0 +3)═(+0 +4)
               ║       ║       ║        ║       ║        ║
    (+1 -3)═(+1 -2)═(+1 -1)═(+1 +0)══(+1 +1)═(+1 +2)══(+1 +3)═(+1 +4)
               ║       ║       ║        ║       ║        ║
    (+2 -3)═(+2 -2)═(+2 -1)═(+2 +0)══(+2 +1)═(+2 +2)══(+2 +3)═(+2 +4)
               ║       ║       ║        ║       ║        ║
            (+3 -2) (+3 -1) (+3 +0)  (+3 +1) (+3 +2)  (+3 +3)