hqs_quantum_solver.spin_util

Utility functions for working with spin systems.

Functions

pure_spin_state(spins[, Sz, mod_Sz, dtype])

Create a representation of a pure spin state for a system of spin-½ particles.

Classes

SpinState(value[, names, module, qualname, ...])

The two states of a spin-½ particle.

class SpinState(value, names=None, *, module=None, qualname=None, type=None, start=1, boundary=None)

The two states of a spin-½ particle.

DOWN = 1

‘Down’ spin state.

UP = 2

‘Up’ spin state.

pure_spin_state(spins: list[SpinState], Sz: int | None = None, mod_Sz: int = 2, dtype: type = np.complex128) → ndarray

Create a representation of a pure spin state for a system of spin-½ particles.

Given a list of single-spin states, i.e., \(\sigma_i \in \{ \downarrow, \uparrow \}\) for \(i = 0, \dots, n-1\), this function returns a representation of the state

\[\ket{\sigma_0 \, \sigma_1 \cdots \sigma_{n-1}} = \ket{\sigma_0} \otimes \ket{\sigma_1} \otimes \cdots \otimes \ket{\sigma_{n-1}} \,.\]

Warning

The values of Sz and mod_Sz need to be the same as in the construction of the operator that this state vector should be used with.

Parameters:

• spins (list[SpinState]) – The list of single-particle spin states.

• Sz (Optional[int]) – The total spin polarization in the z-axis, Sz, in units of ħ/2. abs(Sz) must be less than or equal to the number of sites.

• mod_Sz (int) – Integer representing the extent of Sz violations allowed (in modular arithmetic).

• dtype (type) – The datatype of the state vector to be returned.

Returns:

The state vector.

Return type:

ndarray