SpinHalfFermionSite¶

full name: tenpy.networks.site.SpinHalfFermionSite
parent module: tenpy.networks.site
type: class

Inheritance Diagram

Methods

`SpinHalfFermionSite.__init__`([cons_N, …])	Initialize self.
`SpinHalfFermionSite.add_op`(name, op[, …])	Add one on-site operators.
`SpinHalfFermionSite.change_charge`([…])	Change the charges of the site (in place).
`SpinHalfFermionSite.from_hdf5`(hdf5_loader, …)	Load instance from a HDF5 file.
`SpinHalfFermionSite.get_hc_op_name`(name)	Return the hermitian conjugate of a given operator.
`SpinHalfFermionSite.get_op`(name)	Return operator of given name.
`SpinHalfFermionSite.multiply_op_names`(names)	Multiply operator names together.
`SpinHalfFermionSite.op_needs_JW`(name)	Whether an (composite) onsite operator is fermionic and needs a Jordan-Wigner string.
`SpinHalfFermionSite.remove_op`(name)	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.
`SpinHalfFermionSite.state_index`(label)	Return index of a basis state from its label.
`SpinHalfFermionSite.state_indices`(labels)	Same as `state_index()`, but for multiple labels.
`SpinHalfFermionSite.test_sanity`()	Sanity check, raises ValueErrors, if something is wrong.
`SpinHalfFermionSite.valid_opname`(name)	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]¶

Bases: tenpy.networks.site.Site

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]¶

Add one on-site operators.

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]¶

Remove an added operator.

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

rename_op(old_name, new_name)[source]¶

Rename an added operator.

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 (:class`Group`) – 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: valid – True if name is a valid argument to get_op().
Return type: bool