Create Leg (vector space)#

Tensors are multilinear maps from product of vector spaces. In YASTN, the ‘’legs`` of the tensor represent individual vector spaces.

The spaces of the yastn.Tensor are characterized by a structure yastn.Leg.

class yastn.Leg(sym: any = <class 'yastn.sym.sym_none.sym_none'>, s: int = 1, t: tuple = (), D: tuple = (), fusion: str = 'hard', legs: tuple = (), _verified: bool = False)[source]#

Leg() is a hashable dataclass, defining a vector space.

An abelian symmetric vector space can be specified as a direct sum of plain vector spaces (sectors), each labeled by charge \(t\)

\[V = \bigoplus_t V_t\]

The action of abelian symmetry on elements of such space depends only on the charge \(t\) of the element

\[g \in G:\quad U(g) V = \bigoplus_t U(g)_t V_t.\]

The size of individual sectors \({\rm dim}(V_t)\) is arbitrary.

Parameters:

  • sym (module | _config(NamedTuple)) – YASTN configuration

  • s (int) – Signature of the leg. Either 1 (ingoing) or -1 (outgoing).

  • t (Sequence[int] | Sequence[Sequence[int]]) – List of charge sectors.

  • D (Sequence[int]) – List of dimensions of corresponding charge sectors. The lengths len(D) and len(t) must be equal.

  • legs (Sequence[yastn.Leg]) – Includes information about fused (sub-)legs.

  • fusion (str) – Specification of how the fusion was performed.

__getitem__(t) → int[source]#

Size of a charge sector.

Parameters:

t (int | Sequence[int]) – selected charge sector

conj() → yastn.Leg[source]#

New yastn.Leg with switched signature.

history() → str[source]#

Show linearized representation of Leg fusion history.

'o' marks original legs
's' is for sum, i.e. block
'p' is for product, i.e., fuse_legs(..., mode='hard')
'm' is for meta-fusion

Example

‘p(p(oo)p(oo))’ corresponds to 4 original spaces. Two pairs are fused first, then the result gets fused.

property tD: dict[tuple, int]#

Return charge sectors t and their sizes D as a dictionary {t: D}.

yastn.random_leg(config, s=1, n=None, sigma=1, D_total=8, legs=None, nonnegative=False) → yastn.Leg[source]#

Create yastn.Leg with distributing bond dimensions to sectors randomly according to Gaussian distribution.

Parameters:

  • config (module | _config(NamedTuple)) – YASTN configuration

  • s (int) – Signature of the leg. Either 1 (ingoing) or -1 (outgoing).

  • n (int or tuple) – mean charge of the distribution.

  • sigma (number) – standard deviation of the distribution.

  • D_total (int) – total bond dimension of the leg, to be distributed to sectors.

  • nonnegative (bool) – If True, cut off negative charges.

  • legs (Sequence[yastn.Leg]) – limits charges to match provided legs (e.g., in tensor with zero charge).

yastn.leg_union(*legs) → yastn.Leg[source]#

Output Leg that represent space being an union of spaces of a list of legs.

It collects charges appearing in all provided legs. Their dimensions and fusion history have to match.