Fbit

An object representing a product state of fermionic modes.

This class represents a product state of fermionic modes together with its associated multiplicative coefficient. Each fermionic mode ($\vert 0 \rangle$ or $\vert 1 \rangle$) corresponds respectively to an unoccupied and occupied site. In other words, given the fermionic number operator $n = c^{\dagger} c$, one has that $(\mathbb{I} - 2n) \vert 0 \rangle = \vert 0 \rangle, \quad (\mathbb{I} - 2n)\vert 1 \rangle = \vert 1 \rangle.$ The number of fermionic modes in the product state corresponds to the number of sites on which it has support.

Factories

Fbit(const string bitstring) -> Fbit

Constructs a fermionic product state from a string of consecutive characters "$0$" and "$1$".

Parameters

• bitstring: A string representing the states of the fermionic modes in the product state.

Example

Fbit("00110") // Returns (1 + 0i)|00110>

Fbit(integer num_sites) -> Fbit

Constructs a fermionic product state of size num_sites with every fermionic mode set to $0$.

Parameters

• num_sites: The number of fermionic modes in the product state in a one to one correspondence with the sites.

Example

Fbit(4) // Returns (1 + 0i)|0000>

Fbit(const string bitstring, complex coefficient) -> Fbit

Constructs a fermionic product state from a string of "$0$" and "$1$" with a specified complex multiplicative coefficient.

Parameters

• bitstring: A string representing the states of the fermionic modes in the product state.
• coefficient: The coefficient that multiplies the fermion product state.

Example

Fbit("00110", 2.0 + 5.0i) // Returns (2 + 5i)|00110>

Fbit(const string bitstring, bool coefficient) -> Fbit

Constructs a fermionic product state from a string of "$0$" and "$1$" with a specified bool (converted to complex) multiplicative coefficient.

Parameters

• bitstring: A string representing the states of the fermionic modes in the product state.
• coefficient: The coefficient that multiplies the fermion product state.

Example

Fbit("00110", true) // Returns (1 + 0i)|00110>

Fbit(const string bitstring, real coefficient) -> Fbit

Constructs a fermionic product state from a string of "$0$" and "$1$" with a specified real (converted to complex) multiplicative coefficient.

Parameters

• bitstring: A string representing the states of the fermionic modes in the product state.
• coefficient: The coefficient that multiplies the fermion product state.

Example

Fbit("00110", 2.0) // Returns (2 + 0i)|00110>

Fbit(const string bitstring, integer coefficient) -> Fbit

Constructs a fermionic product state from a string of "$0$" and "$1$" with a specified integer (converted to complex) multiplicative coefficient.

Parameters

• bitstring: A string representing the states of the fermionic modes in the product state.
• coefficient: The coefficient that multiplies the fermion product state.

Example

Fbit("00110", 3) // Returns (3 + 0i)|00110>

Fbit(integer num_sites, complex coefficient) -> Fbit

Constructs a fermionic product state of size num_sites with every fermionic mode set to $0$ with a specified complex multiplicative coefficient.

Parameters

• num_sites: The number of fermionic modes in the product state in a one to one correspondence with the sites.
• coefficient: The coefficient that multiplies the fermion product state.

Example

Fbit(4, 2.0 + 5.0i) // Returns (2 + 5i)|0000>

Fbit(integer num_sites, bool coefficient) -> Fbit

Constructs a fermionic product state of size num_sites with every fermionic mode set to $0$ with a specified bool (converted to complex) multiplicative coefficient.

Parameters

• num_sites: The number of fermionic modes in the product state in a one to one correspondence with the sites.
• coefficient: The coefficient that multiplies the fermion product state.

Example

Fbit(4, true) // Returns (1 + 0i)|0000>

Fbit(integer num_sites, real coefficient) -> Fbit

Constructs a fermionic product state of size num_sites with every fermionic mode set to $0$ with a specified real (converted to complex) multiplicative coefficient.

Parameters

• num_sites: The number of fermionic modes in the product state in a one to one correspondence with the sites.
• coefficient: The coefficient that multiplies the fermion product state.

Example

Fbit(4, 2.0) // Returns (2 + 0i)|0000>

Fbit(integer num_sites, integer coefficient) -> Fbit

Constructs a fermionic product state of size num_sites with every fermionic mode set to $0$ with a specified integer (converted to complex) multiplicative coefficient.

Parameters

• num_sites: The number of fermionic modes in the product state in a one to one correspondence with the sites.
• coefficient: The coefficient that multiplies the fermion product state.

Example

Fbit(4, 3) // Returns (3 + 0i)|0000>

Symbols

Name	Description
=	Assignment operator for Fbit objects.
[]	Returns the state of the fermionic mode (interpreted as an integer) at the specified site.

Members

Name	Description
count	Returns the sum of the occupation numbers of a subset of sites (interpreted as integers) in the product state.
create	Applies the creation operator $c_i^{\dagger}$ on the fermionic product state in place.
created	Returns a copy of the product state on which the creation operator $c_i^{\dagger}$ was applied.
destroy	Applies the annihilation operator $c_i$ on the fermionic product state in place.
destroyed	Returns a copy of the product state on which the annihilation operator $c_i$ was applied.
flip	This method modifies the Fbit object in place by flipping the state of the fermionic modes at the specified sites.
flipped	Returns a copy of the product state with the fermionic mode at the specified site flipped.
get_state	Returns the state of the fermionic mode (interpreted as an integer) at the specified site.
insert	Inserts a fermionic mode set to 0 at the specified site.
inserted	Returns a copy of the product state with a fermionic mode in the "$0$" state inserted on the left of the fermionic mode at the specified site.
period	Returns the number of times the fermionic modes have to be circularly shifted to the right by a number of sites equal to the provided integer before the obtained product state is equal to the starting product state.
reflect	Reverses the product state (reversed end-to-end) in place.
reflected	Returns a copy of the reflected (reversed end-to-end) product state.
set_representation	Sets the integer representation of the Fbit.
split	Splits the product state into a pair of Fbit objects according to a specified set of states for the resulting left and right product state.
swap	This methods swaps the fermionic modes of the product state at the specified sites in place.
swapped	Returns a copy of the Fbit object with two specified fermionic modes swapped.
translate	Circularly shifts in place the fermionic modes of the product state by $1$ site to the right.
translated	Returns a copy of the product state with its fermionic modes shifted by $1$ site to the right.