# SpinHalfSite

Inheritance Diagram

Methods

 SpinHalfSite.__init__([conserve, sort_charge]) SpinHalfSite.add_op(name, op[, need_JW, hc, ...]) Add one on-site operators. SpinHalfSite.change_charge([new_leg_charge, ...]) Change the charges of the site (in place). Convert charge values to Jordan-Wigner parity. SpinHalfSite.from_hdf5(hdf5_loader, h5gr, ...) Load instance from a HDF5 file. Return the hermitian conjugate of a given operator. Return operator of given name. Multiply operator names together. SpinHalfSite.multiply_operators(operators) Multiply local operators (possibly given by their names) together. Whether an (composite) onsite operator is fermionic and needs a Jordan-Wigner string. Remove an added operator. SpinHalfSite.rename_op(old_name, new_name) Rename an added operator. SpinHalfSite.save_hdf5(hdf5_saver, h5gr, subpath) Export self into a HDF5 file. SpinHalfSite.sort_charge([bunch]) Sort the leg charges (in place). Return index of a basis state from its label. Same as state_index(), but for multiple labels. Sanity check, raises ValueErrors, if something is wrong. Check whether 'name' labels a valid onsite-operator.

Class Attributes and Properties

 SpinHalfSite.dim Dimension of the local Hilbert space. SpinHalfSite.onsite_ops Dictionary of on-site operators for iteration.
class tenpy.networks.site.SpinHalfSite(conserve='Sz', sort_charge=True)[source]

Bases: Site

Spin-1/2 site.

Local states are up (0) and down (1). Local operators are the usual spin-1/2 operators, e.g. Sz = [[0.5, 0.], [0., -0.5]], Sx = 0.5*sigma_x for the Pauli matrix sigma_x.

operator

description

Id, JW

Identity $$\mathbb{1}$$

Sx, Sy, Sz

Spin components $$S^{x,y,z}$$, equal to half the Pauli matrices.

Sigmax, Sigmay, Sigmaz

Pauli matrices $$\sigma^{x,y,z}$$

Sp, Sm

Spin flips $$S^{\pm} = S^{x} \pm i S^{y}$$

conserve

qmod

excluded onsite operators

'Sz'

[1]

Sx, Sy, Sigmax, Sigmay

'parity'

[2]

'None'

[]

Parameters:
• conserve (str | None) – Defines what is conserved, see table above.

• sort_charge (bool) – Whether sort_charge() should be called at the end of initialization. This is usually a good idea to reduce potential overhead when using charge conservation. Note that this permutes the order of the local basis states!

conserve

Defines what is conserved, see table above.

Type:

str

Parameters:
• name (str) – A valid python variable name, used to label the operator. The name under which op is added as attribute to self.

• op (np.ndarray | Array) – A matrix acting on the local hilbert space representing the local operator. Dense numpy arrays are automatically converted to Array. LegCharges have to be [leg, leg.conj()]. We set labels 'p', 'p*'.

• need_JW (bool) – Whether the operator needs a Jordan-Wigner string. If True, add name to need_JW_string.

• hc (None | False | str) – The name for the hermitian conjugate operator, to be used for hc_ops. By default (None), try to auto-determine it. If False, disable adding entries to hc_ops.

• permute_dense (bool | None) – Flag to enable/disable permutations when converting op from numpy to np_conserved arrays. If True, the operator is permuted with perm to account for permutations induced by sorting charges; False disables the permutations. By default (None), the value of used_sort_charge is used.

change_charge(new_leg_charge=None, permute=None)[source]

Change the charges of the site (in place).

Parameters:
• new_leg_charge (LegCharge | None) – The new charges to be used. If None, use trivial charges.

• permute (ndarray | None) – The permutation applied to the physical leg, which also gets used to adjust state_labels and perm. If you sorted the previous leg with perm_qind, new_leg_charge = leg.sort(), use old_leg.perm_flat_from_perm_qind(perm_qind). Ignored if None.

charge_to_JW_signs(charges)[source]

Convert charge values to Jordan-Wigner parity.

Often, charge conservation contains the (parity of) the total fermion number. This information is enough to lift a Jordan-Wigner string applied on the left of a given bond to the virtual leg of an MPS: given the total parity number of fermions parity[alpha] = N_fermions[alpha] % 2 in each Schmidt state |alpha>, simply send |alpha> --> (-1)**parity[alpha] |alpha>. Given the charges values of the Schmidt states |alpha>, this function returns the corresponding (-1)**parity Jordan-Wigner signs.

Parameters:

charges (2D or 1D array) – Charge values, last dimension is len chinfo.qnumber. We choose the convention that these charge values correspond to an “incoming” leg with qconj=+1.

Returns:

Should only have values +1 or -1.

Return type:

JW_signs

property dim

Dimension of the local Hilbert space.

Load instance from a HDF5 file.

This method reconstructs a class instance from the data saved with save_hdf5().

Parameters:
• hdf5_loader (Hdf5Loader) – Instance of the loading engine.

• h5gr (Group) – HDF5 group which is represent the object to be constructed.

• subpath (str) – The name of h5gr with a '/' in the end.

Returns:

obj – Newly generated class instance containing the required data.

Return type:

cls

get_hc_op_name(name)[source]

Return the hermitian conjugate of a given operator.

Parameters:

name (str) – The name of the operator to be conjugated. Multiple operators separated by whitespace are interpreted as an operator product, exactly as get_op() does.

Returns:

hc_op_name – Operator name for the hermitian conjugate operator.

Return type:

str

get_op(name)[source]

Return operator of given name.

Parameters:

name (str) – The name of the operator to be returned. In case of multiple operator names separated by whitespace, we multiply them together to a single on-site operator (with the one on the right acting first).

Returns:

op – The operator given by name, with labels 'p', 'p*'. If name already was an npc Array, it’s directly returned.

Return type:

np_conserved

multiply_op_names(names)[source]

Multiply operator names together.

Join the operator names in names such that get_op returns the product of the corresponding operators.

Parameters:

names (list of str) – List of valid operator labels.

Returns:

combined_opname – A valid operator name Operator name representing the product of operators in names.

Return type:

str

multiply_operators(operators)[source]

Multiply local operators (possibly given by their names) together.

Parameters:

operators (list of {str | Array}) – List of valid operator names (to be translated with get_op()) or directly on-site operators in the form of npc arrays with 'p', 'p*' label. The operators are multiplied left-to-right.

Returns:

combined_operator – The product of the given operators in a left-to-right multiplication following the usual mathematical convention. For example, if operators=['Sz', 'Sp', 'Sx'], the final operator is equivalent to site.get_op('Sz Sp Sx'), with the 'Sx' operator acting first on any physical state.

Return type:

Array

property onsite_ops

Dictionary of on-site operators for iteration.

Single operators are accessible as attributes.

op_needs_JW(name)[source]

Whether an (composite) onsite operator is fermionic and needs a Jordan-Wigner string.

Parameters:

name (str) – The name of the operator, as in get_op().

Returns:

needs_JW – Whether the operator needs a Jordan-Wigner string, judging from need_JW_string.

Return type:

bool

remove_op(name)[source]

Parameters:

name (str) – The name of the operator to be removed.

rename_op(old_name, new_name)[source]

Parameters:
• old_name (str) – The old name of the operator.

• new_name (str) – The new name of the operator.

save_hdf5(hdf5_saver, h5gr, subpath)[source]

Export self into a HDF5 file.

This method saves all the data it needs to reconstruct self with from_hdf5().

This implementation saves the content of __dict__ with save_dict_content(), storing the format under the attribute 'format'.

Parameters:
• hdf5_saver (Hdf5Saver) – Instance of the saving engine.

• h5gr (:classGroup) – HDF5 group which is supposed to represent self.

• subpath (str) – The name of h5gr with a '/' in the end.

sort_charge(bunch=True)[source]

Sort the leg charges (in place).

Parameters:

bunch (bool) – Whether to also group equal charges into larger blocks (usually a good idea).

Returns:

perm – The permutation

Return type:

1D ndarray

state_index(label)[source]

Return index of a basis state from its label.

Parameters:

label (int | string) – either the index directly or a label (string) set before.

Returns:

state_index – the index of the basis state associated with the label.

Return type:

int

state_indices(labels)[source]

Same as state_index(), but for multiple labels.

test_sanity()[source]

Sanity check, raises ValueErrors, if something is wrong.

valid_opname(name)[source]

Check whether ‘name’ labels a valid onsite-operator.

Parameters:

name (str) – Label for the operator. Can be multiple operator(labels) separated by whitespace, indicating that they should be multiplied together.

Returns:

validTrue if name is a valid argument to get_op().

Return type:

bool