Site¶

Inheritance Diagram

Methods

 Site.__init__(leg[, state_labels]) Initialize self. Site.add_op(name, op[, need_JW, hc]) Add one on-site operators. Site.change_charge([new_leg_charge, permute]) Change the charges of the site (in place). Site.from_hdf5(hdf5_loader, h5gr, subpath) Load instance from a HDF5 file. Return the hermitian conjugate of a given operator. Site.get_op(name) Return operator of given name. Multiply operator names together. Whether an (composite) onsite operator is fermionic and needs a Jordan-Wigner string. Site.remove_op(name) Remove an added operator. Site.rename_op(old_name, new_name) Rename an added operator. Site.save_hdf5(hdf5_saver, h5gr, subpath) Export self into a HDF5 file. Site.state_index(label) Return index of a basis state from its label. Site.state_indices(labels) 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

 Site.dim Dimension of the local Hilbert space. Site.onsite_ops Dictionary of on-site operators for iteration.
class tenpy.networks.site.Site(leg, state_labels=None, **site_ops)[source]

Collects necessary information about a single local site of a lattice.

This class defines what the local basis states are: it provides the leg defining the charges of the physical leg for this site. Moreover, it stores (local) on-site operators, which are directly available as attribute, e.g., self.Sz is the Sz operator for the SpinSite. Alternatively, operators can be obained with get_op(). The operator names Id and JW are reserved for the identy and Jordan-Wigner strings.

Warning

The order of the local basis can change depending on the charge conservation! This is a necessary feature since we need to sort the basis by charges for efficiency. We use the state_labels and perm to keep track of these permutations.

Parameters
• leg (LegCharge) – Charges of the physical states, to be used for the physical leg of MPS.

• state_labels (None | list of str) – Optionally a label for each local basis states. None entries are ignored / not set.

• **site_ops – Additional keyword arguments of the form name=op given to add_op(). The identity operator 'Id' is automatically included. If no 'JW' for the Jordan-Wigner string is given, 'JW' is set as an alias to 'Id'.

leg

Charges of the local basis states.

Type

LegCharge

state_labels

(Optional) labels for the local basis states.

Type

{str: int}

opnames

Labels of all onsite operators (i.e. self.op exists if 'op' in self.opnames). Note that get_op() allows arbitrary concatenations of them.

Type

set

need_JW_string

Labels of all onsite operators that need a Jordan-Wigner string. Used in op_needs_JW() to determine whether an operator anticommutes or commutes with operators on other sites.

Type

set

ops

Onsite operators are added directly as attributes to self. For example after self.add_op('Sz', Sz) you can use self.Sz for the Sz operator. All onsite operators have labels 'p', 'p*'.

Type

Array

perm

Index permutation of the physical leg compared to conserve=None, i.e. OP_conserved = OP_nonconserved[np.ix_(perm,perm)] and perm[state_labels_conserved["some_state"]] == state_labels_nonconserved["some_state"].

Type

1D array

JW_exponent

Exponents of the 'JW' operator, such that self.JW.to_ndarray() = np.diag(np.exp(1.j*np.pi* JW_exponent))

Type

1D array

hc_ops

Mapping from operator names to their hermitian conjugates. Use get_hc_op_name() to obtain entries.

Type

dict(str->str)

Examples

The following generates a site for spin-1/2 with Sz conservation. Note that Sx = (Sp + Sm)/2 violates Sz conservation and is thus not a valid on-site operator.

>>> chinfo = npc.ChargeInfo([1], ['Sz'])
>>> ch = npc.LegCharge.from_qflat(chinfo, [1, -1])
>>> Sp = [[0, 1.], [0, 0]]
>>> Sm = [[0, 0], [1., 0]]
>>> Sz = [[0.5, 0], [0, -0.5]]
>>> site = Site(ch, ['up', 'down'], Splus=Sp, Sminus=Sm, Sz=Sz)
>>> print(site.Splus.to_ndarray())
array([[ 0.,  1.],
[ 0.,  0.]])
>>> print(site.get_op('Sminus').to_ndarray())
array([[ 0.,  0.],
[ 1.,  0.]])
>>> print(site.get_op('Splus Sminus').to_ndarray())
array([[ 1.,  0.],
[ 0.,  0.]])

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 permuation applied to the physical leg, which 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.

test_sanity()[source]

Sanity check, raises ValueErrors, if something is wrong.

property dim

Dimension of the local Hilbert space.

property onsite_ops

Dictionary of on-site operators for iteration.

Single operators are accessible as attributes.

add_op(name, op, need_JW=False, hc=None)[source]

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 antries to hc_ops.

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.

remove_op(name)[source]

Parameters

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

state_index(label)[source]

Return index of a basis state from its label.

Parameters

label (int | string) – eather 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.

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

get_hc_op_name(name)[source]

Return the hermitian conjugate of a given operator.

Parameters

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

Returns

hc_op_name – Operator name for the hermi such that get_op() of

Return type

str

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

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

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 Operatorname representing the product of operators in names.

Return type

str

classmethod from_hdf5(hdf5_loader, h5gr, subpath)[source]

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

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.