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: int | tuple[int, int] | None = 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: spin, spinful fermion, or spinless fermion. Specify it with a PARTICLE_TYPE member, or equivalently its name as a string (e.g. "spinful_fermion").

  • Nparticles – The number of particles in the system. If unspecified, the particle number is non-conserved, except spin systems which default to Nsites (i.e. no magnetization conservation, since the total spin count is always Nsites). If specified, use an int for the total particle number, or a tuple (n_up, n_dn) for the number of spin-up and spin-down particles. For spin systems the total is always Nsites, so a magnetization sector must be fixed with a tuple (n_up, n_dn) summing to Nsites rather than an int.

  • 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 length of a configuration array, i.e. the number of local degrees of freedom stored per sample. This is Nsites for spins or spinless fermions and 2 * Nsites for spinful fermions (one entry per spin-up and spin-down mode).

property Nfmodes: int#

The number of fermionic modes, which should be Nsites for spinless fermions and 2 * Nsites for spin and spinful fermions. This is used when a system is mapped to a fermionic representation (e.g. mean-field or backflow states), where a spin maps to two fermionic modes (spin-up and spin-down) per site.

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

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 particle_type: PARTICLE_TYPE#

The type of particle in the system. See PARTICLE_TYPE.

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[float64]#

Real space coordinates of all sites.

property dist: NDArray[float64]#

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[int64]#

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 = 1, return_sign: Literal[False] = False) → NDArray[int64]#
get_neighbor(n_neighbor: int, return_sign: Literal[True]) → tuple[NDArray[int64], NDArray[int64]]
get_neighbor(n_neighbor: Sequence[int], return_sign: Literal[False] = False) → list[NDArray[int64]]
get_neighbor(n_neighbor: Sequence[int], return_sign: Literal[True]) → tuple[list[NDArray[int64]], list[NDArray[int64]]]

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 indices. If n_neighbor is sequence, then a list with each item a 2D numpy array corresponding to n_neighbor items. If the requested n’th-nearest neighbor doesn’t exist in the system, the corresponding array is empty.

sign

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

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

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.