Correlation functions¶
- ctm.one_site_c4v_abelian.corrf_c4v.apply_TM_1sO(state, env, edge, op=None, verbosity=0)[source]¶
- Parameters:
state (IPEPS_C4V_ABELIAN) – underlying 1-site C4v symmetric wavefunction
env (ENV_C4V_ABELIAN) – C4v symmetric environment corresponding to
state
edge (yastn.Tensor) – tensor corresponding to the edge of width-1 channel
op (yastn.Tensor) – operator to be inserted into transfer matrix
verbosity (int) – logging verbosity
- Returns:
edge
with a single instance of the transfer matrix applied. The resulting tensor has an identical index structure as the originaledge
- Return type:
tensor
Applies a single instance of the “transfer matrix” to the
edge
tensor by contracting the following network:-----T---------- | | edge--(a^+ op a)-- | | -----T----------
where the physical indices s and s’ of the on-site tensor \(a\) and it’s hermitian conjugate \(a^\dagger\) are contracted with identity \(\delta_{s,s'}\) or
op
(if supplied).
- ctm.one_site_c4v_abelian.corrf_c4v.apply_edge(state, env, vec, verbosity=0)[source]¶
- Parameters:
state (IPEPS_ABELIAN_C4V) – underlying 1-site C4v symmetric wavefunction
env (ENV_ABELIAN_C4V) – C4v symmetric environment corresponding to
state
vec (torch.Tensor) – tensor of dimensions \(\chi \times D^2 \times \chi\)
verbosity (int) – logging verbosity
- Returns:
scalar resulting from the contraction of
vec
with an edge built from environment- Return type:
torch.tensor
Contracts
vec
tensor with the corresponding edge by contracting the following network:---C | | scalar = vec--T | | ---C
- ctm.one_site_c4v_abelian.corrf_c4v.corrf_1sO1sO(state, env, op1, get_op2, dist, verbosity=0)[source]¶
- Parameters:
state (IPEPS_ABELIAN_C4V) – underlying 1-site C4v symmetric wavefunction
env (ENV_ABELIAN_C4V) – C4v symmetric environment corresponding to
state
op1 (yastn.Tensor) – first one-site operator \(O_1\)
get_op2 (function(int)->yastn.Tensor) – function returning (position-dependent) second one-site opreator \(\text{get_op2}(r)=O_2\)
dist (int) – maximal distance of correlation function
verbosity (int) – logging verbosity
- Returns:
vector
corrf
of lengthdist
holding the values of correlation function \(\langle O_1(0) O_2(r) \rangle\) for \(r \in [1,dist]\)- Return type:
torch.tensor
Computes the two-point correlation function \(\langle O_1(0) O_2(r) \rangle\) by contracting the following network:
C-----T---------- ... -----T---- ... --------T-------------C | | | | | T--(a^+ op_1 a)-- ... --(a^+a)-- ... --(a^+ gen_op2(r) a)--T | | | | | C-----T---------- ... -----T---- ... --------T-------------C
for increasingly large distance
r
up todist
.
- ctm.one_site_c4v_abelian.corrf_c4v.get_edge(state, env, verbosity=0)[source]¶
- Parameters:
state (IPEPS_C4V_ABELIAN) – underlying 1-site C4v symmetric wavefunction
env (ENV_C4V_ABELIAN) – C4v symmetric environment corresponding to
state
verbosity (int) – logging verbosity
- Returns:
edge of the width-1 channel
- Return type:
Tensor
Build initial edge by contracting the following network:
C--0(-) | E = T--1(-) 1,2 | C--2(-) 3