MultiCouplingTerms¶

full name: tenpy.networks.terms.MultiCouplingTerms
parent module: tenpy.networks.terms
type: class

class tenpy.networks.terms.MultiCouplingTerms(L)[source]¶

Bases: tenpy.networks.terms.CouplingTerms

Operator names, site indices and strengths representing general M-site coupling terms.

Generalizes the coupling_terms of CouplingTerms to M-site couplings. The structure of the nested dictionary coupling_terms is similar, but we allow an arbitrary recursion depth of the dictionary.

Parameters

Lint: Number of sites.

Attributes

Lint

Number of sites.

coupling_termsdict of dict

Nested dictionaries of the following form:

{i: {('opname_i', 'opname_string_ij'):
        {j: {('opname_j', 'opname_string_jk'):
                {k: {('opname_k', 'opname_string_kl'):
                    ...
                        {l: {'opname_l':
                                strength
                        }   }
                    ...
                }   }
        }   }
}   }

For a M-site coupling, this involves a nesting depth of 2*M dictionaries. Note that always i < j < k < ... < l, but entries with j,k,l >= L are allowed for the case of bc_MPS == 'infinite', when they indicate couplings between different iMPS unit cells.

Methods

`add_coupling_term`(self, strength, i, j, …)	Add a two-site coupling term on given MPS sites.
`add_multi_coupling_term`(self, strength, …)	Add a multi-site coupling term.
`add_to_graph`(self, graph[, _i, _d1, _label_left])	Add terms from `coupling_terms` to an MPOGraph.
`coupling_term_handle_JW`(self, strength, …)	Helping function to call before `add_multi_coupling_term()`.
`max_range`(self)	Determine the maximal range in `coupling_terms`.
`multi_coupling_term_handle_JW`(self, …[, …])	Helping function to call before `add_multi_coupling_term()`.
`plot_coupling_terms`(self, ax, lat[, …])	“Plot coupling terms into a given lattice.
`remove_zeros`(self[, tol_zero, _d0])	Remove entries close to 0 from `coupling_terms`.
`to_TermList`(self)	Convert `onsite_terms` into a `TermList`.
`to_nn_bond_Arrays`(self, sites)	Convert the `coupling_terms` into Arrays on nearest neighbor bonds.

add_multi_coupling_term(self, strength, ijkl, ops_ijkl, op_string='Id')[source]¶

Add a multi-site coupling term.

Parameters

strengthfloat: The strength of the coupling term.
ijkllist of int: The MPS indices of the sites on which the operators acts. With i, j, k, … = ijkl, we require that they are ordered ascending, i < j < k < ... and that 0 <= i < N_sites. Inidces >= N_sites indicate couplings between different unit cells of an infinite MPS.
ops_ijkllist of str: Names of the involved operators on sites i, j, k, ….
op_string(list of) str: Names of the operator to be inserted between the operators, e.g., op_string[0] is inserted between i and j. A single name holds for all in-between segments.

multi_coupling_term_handle_JW(self, strength, term, sites, op_string=None)[source]¶

Helping function to call before add_multi_coupling_term().

Handle/figure out Jordan-Wigner strings if needed.

Parameters

strengthfloat: The strength of the term.
termlist of (str, int): List of tuples (op_i, i) where i is the MPS index of the site the operator named op_i acts on. We require the operators to be sorted (strictly ascending) by sites. If necessary, call order_combine_term() beforehand.
siteslist of Site: Defines the local Hilbert space for each site. Used to check whether the operators need Jordan-Wigner strings.
op_stringNone | str: Operator name to be used as operator string between the operators, or None if the Jordan Wigner string should be figured out.

Returns

strength, ijkl, ops_ijkl, op_string :: Arguments for MultiCouplingTerms.add_multi_coupling_term() such that the added term corresponds to the parameters of this function.

max_range(self)[source]¶

Determine the maximal range in coupling_terms.

Returns

max_rangeint: The maximum of j - i for the i, j occuring in a term of coupling_terms.

add_to_graph(self, graph, _i=None, _d1=None, _label_left=None)[source]¶

Add terms from coupling_terms to an MPOGraph.

Parameters

graphMPOGraph: The graph into which the terms from coupling_terms should be added.
_i, _d1, _label_leftNone: Should not be given; only needed for recursion.

remove_zeros(self, tol_zero=1e-15, _d0=None)[source]¶

Remove entries close to 0 from coupling_terms.

Parameters

tol_zerofloat: Entries in coupling_terms with strength < tol_zero are considered to be zero and removed.
_d0None: Should not be given; only needed for recursion.

to_TermList(self)[source]¶

Convert onsite_terms into a TermList.

Returns

term_listTermList: Representation of the terms as a list of terms.

add_coupling_term(self, strength, i, j, op_i, op_j, op_string='Id')¶

Add a two-site coupling term on given MPS sites.

Parameters

strengthfloat: The strength of the coupling term.
i, jint: The MPS indices of the two sites on which the operator acts. We require 0 <= i < N_sites and i < j, i.e., op_i acts “left” of op_j. If j >= N_sites, it indicates couplings between unit cells of an infinite MPS.
op1, op2str: Names of the involved operators.
op_stringstr: The operator to be inserted between i and j.

coupling_term_handle_JW(self, strength, term, sites, op_string=None)¶

Helping function to call before add_multi_coupling_term().

Parameters

strengthfloat: The strength of the coupling term.
term[(str, int), (str, int)]: List of two tuples (op, i) where i is the MPS index of the site the operator named op acts on.
siteslist of Site: Defines the local Hilbert space for each site. Used to check whether the operators need Jordan-Wigner strings.
op_stringNone | str: Operator name to be used as operator string between the operators, or None if the Jordan Wigner string should be figured out.

Returns

strength, i, j, op_i, op_j, op_string:: Arguments for MultiCouplingTerms.add_multi_coupling_term() such that the added term corresponds to the parameters of this function.

plot_coupling_terms(self, ax, lat, style_map='default', common_style={'linestyle': '--'}, text=None, text_pos=0.4)¶

“Plot coupling terms into a given lattice.

This function plots the coupling_terms

Parameters

axmatplotlib.axes.Axes: The axes on which we should plot.
latLattice: The lattice for plotting the couplings, most probably the M.lat of the corresponding model M, see lat.
style_mapfunction | None: Function which get’s called with arguments i, j, op_i, op_string, op_j, strength for each two-site coupling and should return a keyword-dictionary with the desired plot-style for this coupling. By default (None), the linewidth is given by the absolute value of strength, and the linecolor depends on the phase of strength (using the hsv colormap).
common_styledict: Common style, which overwrites values of the dictionary returned by style_map. A 'label' is only used for the first plotted line.
text: format_string | None: If not None, we add text labeling the couplings in the plot. Available keywords are i, j, op_i, op_string, op_j, strength as well as strength_abs, strength_angle, strength_real.
text_posfloat: Specify where to put the text on the line between i (0.0) and j (1.0), e.g. 0.5 is exactly in the middle between i and j.