# SpinHalfFermionSite¶

Inheritance Diagram

Methods

 SpinHalfFermionSite.__init__([cons_N, …]) Initialize self. SpinHalfFermionSite.add_op(name, op[, …]) Add one on-site operators. Change the charges of the site (in place). SpinHalfFermionSite.from_hdf5(hdf5_loader, …) Load instance from a HDF5 file. Return the hermitian conjugate of a given operator. Return operator of given name. Multiply operator names together. Whether an (composite) onsite operator is fermionic and needs a Jordan-Wigner string. Remove an added operator. SpinHalfFermionSite.rename_op(old_name, new_name) Rename an added operator. SpinHalfFermionSite.save_hdf5(hdf5_saver, …) Export self into a HDF5 file. 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

 SpinHalfFermionSite.dim Dimension of the local Hilbert space. SpinHalfFermionSite.onsite_ops Dictionary of on-site operators for iteration.
class tenpy.networks.site.SpinHalfFermionSite(cons_N='N', cons_Sz='Sz', filling=1.0)[source]

Create a Site for spinful (spin-1/2) fermions.

Local states are:

empty (vacuum), up (one spin-up electron), down (one spin-down electron), and full (both electrons)

Local operators can be built from creation operators.

Warning

Using the Jordan-Wigner string (JW) in the correct way is crucial to get correct results, otherwise you just describe hardcore bosons!

operator

description

Id

Identity $$\mathbb{1}$$

JW

Sign for the Jordan-Wigner string $$(-1)^{n_{\uparrow}+n_{\downarrow}}$$

JWu

Partial sign for the Jordan-Wigner string $$(-1)^{n_{\uparrow}}$$

JWd

Partial sign for the Jordan-Wigner string $$(-1)^{n_{\downarrow}}$$

Cu

Annihilation operator spin-up $$c_{\uparrow}$$ (up to ‘JW’-string on sites left of it).

Cdu

Creation operator spin-up $$c^\dagger_{\uparrow}$$ (up to ‘JW’-string on sites left of it).

Cd

Annihilation operator spin-down $$c_{\downarrow}$$ (up to ‘JW’-string on sites left of it). Includes JWu such that it anti-commutes onsite with Cu, Cdu.

Cdd

Creation operator spin-down $$c^\dagger_{\downarrow}$$ (up to ‘JW’-string on sites left of it). Includes JWu such that it anti-commutes onsite with Cu, Cdu.

Nu

Number operator $$n_{\uparrow}= c^\dagger_{\uparrow} c_{\uparrow}$$

Nd

Number operator $$n_{\downarrow}= c^\dagger_{\downarrow} c_{\downarrow}$$

NuNd

Dotted number operators $$n_{\uparrow} n_{\downarrow}$$

Ntot

Total number operator $$n_t= n_{\uparrow} + n_{\downarrow}$$

dN

Total number operator compared to the filling $$\Delta n = n_t-filling$$

Sx, Sy, Sz

Spin operators $$S^{x,y,z}$$, in particular $$S^z = \frac{1}{2}( n_\uparrow - n_\downarrow )$$

Sp, Sm

Spin flips $$S^{\pm} = S^{x} \pm i S^{y}$$, e.g. $$S^{+} = c^\dagger_\uparrow c_\downarrow$$

The spin operators are defined as $$S^\gamma = (c^\dagger_{\uparrow}, c^\dagger_{\downarrow}) \sigma^\gamma (c_{\uparrow}, c_{\downarrow})^T$$, where $$\sigma^\gamma$$ are spin-1/2 matrices (i.e. half the pauli matrices).

cons_N

cons_Sz

qmod

excluded onsite operators

'N'

'Sz'

[1, 1]

Sx, Sy

'N'

'parity'

[1, 2]

'N'

None

[1]

'parity'

'Sz'

[2, 1]

Sx, Sy

'parity'

'parity'

[2, 2]

'parity'

None

[2]

None

'Sz'

[1]

Sx, Sy

None

'parity'

[2]

None

None

[]

Todo

Check if Jordan-Wigner strings for 4x4 operators are correct.

Parameters
• cons_N ('N' | 'parity' | None) – Whether particle number is conserved, c.f. table above.

• cons_Sz ('Sz' | 'parity' | None) – Whether spin is conserved, c.f. table above.

• filling (float) – Average filling. Used to define dN.

cons_N

Whether particle number is conserved, c.f. table above.

Type

'N' | 'parity' | None

cons_Sz

Whether spin is conserved, c.f. table above.

Type

'Sz' | 'parity' | None

filling

Average filling. Used to define dN.

Type

float

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.

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.

property dim

Dimension of the local Hilbert space.

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

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

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 Operatorname representing the product of operators in names.

Return type

str

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.

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.

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