quantax.sites.Sites#

class quantax.sites.Sites#

A collection of multiple spins or fermions that make up the quantum system.

__init__(Nsites: int, particle_type: PARTICLE_TYPE | str = PARTICLE_TYPE.spin, Nparticles: None | int | Tuple[int, int] = None, double_occ: bool | None = None, coord: ndarray | None = None)#
Parameters:

  • Nsites – The number of sites in the system.

  • particle_type – The particle type of the system, including spin, spinful fermion, and spinless fermion. Please specify one type using PARTICLE_TYPE.

  • Nparticles – The number of particles in the system. If unspecified, the number of particles is non-conserved. If specified, use an int to specify the total particle number, or use a tuple (n_up, n_dn) to specify the number of spin-up and spin-down particles.

  • double_occ – Whether double occupancy is allowed. Default to True for spinful fermions and False otherwise.

  • coord – The coordinates of sites, which doesn’t have to be specified if the spatial information is not used.

property Nsites: int#

The number of sites

property Nmodes: int#

The number of qubit degrees of freedom, which should be Nsites for spins or spinless fermions and 2 * Nsites for spinful fermions.

property Nfmodes: int#

The number of fermionic modes, which should be Nsites for spinless fermions and 2 * Nsites for spin and spinful fermions.

property Nparticles: None | int | Tuple[int, int]#

The number of particles.

  • None: No particle conservation.

  • int: Conservation of total particle number.

  • Tuple[int, int]: Conservation of spin-up and spin-down particle numbers.

property Ntotal: int | None#

The total number of particles.

property ndim: int#

The number of spatial dimensions, e.g., 2 for square lattice and 3 for cubic.

property double_occ: bool#

Whether the system allows double occupancy.

property is_fermion: bool#

Whether the system is made of fermions.

property is_spinful: bool#

Whether the system is spinful.

property coord: ndarray#

Real space coordinates of all sites.

property dist: ndarray#

Matrix of the real space distance between all site pairs.

Tip

dist[2, 3] is the distance between site 2 and 3.

property sign: ndarray#

Matrix of the sign between all site pairs. For example, in a fermionic system with anti-periodic boundary conditions, the sign of bonds crossing the boundary is -1, while other bonds have sign +1.

Tip

sign[2, 3] is the sign of the bond connecting site 2 and 3.

get_neighbor(n_neighbor: int | Sequence[int] = 1, return_sign: bool = False) → ndarray | Sequence[ndarray] | tuple#

Gets n’th-nearest neighbor site pairs.

Parameters:

  • n_neighbor – The n’th-nearest neighbor to obtain. The nearest neighbor is given by 1. If it’s a sequence, then multiple neighbors will be returned in the same order.

  • return_sign – Whether this function should also return the sign of neighbor bonds. The sign is non-trivial only for fermionic systems with anti-periodic boundary conditions.

Returns:

neighbor

If n_neighbor is int, then a 2D numpy array with each row a pair of neighbor site indeces. If n_neighbor is sequence, then a list with each item a 2D numpy array corresponding to n_neighbor items.

sign

The sign of neighbor bonds. Only provided if return_sign is True.

plot(figsize: Sequence[int | float] = (10, 10), markersize: int | float | None = None, color: str | Sequence[str] = 'C0', show_index: bool = True, index_fontsize: int | float | None = None, neighbor_bonds: int | Sequence[int] = 1)#

Plot the sites and neighbor bonds in the real space.

Parameters:

  • figsize – Figure size.

  • markersize – Size of markers that represent the sites.

  • color – Color of sites in the figure.

  • show_index – Whether to show index number at each site.

  • index_fontsize – Fontsize if the index number is shown.

  • neighbor_bonds – The n’th-nearest neighbor bonds to show. Set this value to 0 to hide all bonds.

Returns:

A matplotlib figure containing the geometrical plot of sites.