#!/usr/bin/env python3
from functools import cached_property
from functools import lru_cache as cached
import numpy as np
import torch
from tdg.h5 import H5able
[docs]class Potential(H5able):
r'''
A potential encodes a term in the many-body Hamiltonian like :math:`nVn`, where :math:`n` are number operators and :math:`V` can connect
different sites.
A potential is built up from one or more LegoSpheres :math:`\mathcal{S}^{\vec{R}}`, each which carries its own Wilson coefficient :math:`C_\vec{R}`,
.. math::
\tilde{V} = N_x^2 \sum_R C_R \mathcal{S}^R
'''
def __init__(self, *spheres):
self.spheres = [*spheres]
def __str__(self):
return f"Potential({', '.join([str(s) for s in self.spheres])})"
def __repr__(self):
return str(self)
[docs] @cached
def spatial(self, lattice):
r'''
Parameters
----------
lattice: tdg.Lattice
Returns
-------
torch.tensor:
A matrix encoding :math:`V` on the given lattice. The two axes of the matrix are in the order of the lattice :attr:`~.Lattice.coordinates`.
'''
return lattice.sites * torch.sum(torch.stack([s.spatial(lattice) for s in self.spheres]), axis=0)
[docs] @cached
def inverse(self, lattice):
r'''
Parameters
----------
lattice: tdg.Lattice
Returns
-------
torch.tensor:
The inverse matrix of ``spatial(lattice)``.
'''
return torch.linalg.inv(self.spatial(lattice))
[docs] @cached
def eigvals(self, lattice):
r'''
Parameters
----------
lattice: tdg.Lattice
Returns
-------
torch.tensor:
An array of eigenvalues of ``spatial(lattice)``. If any of the eigenvalues are imaginary, raises a TypeError; the potential should be Hermitian.
Raises a ValueError if any of the eigenvalues are positive; we require the attractive channel.
'''
e = torch.linalg.eigvals(self.spatial(lattice))
if (e.imag != 0).all():
raise TypeError(f"{self} yields imaginary eigenvalues.")
if (e.real >= 0).any():
raise ValueError(f"{self} yields positive eigenvalues; we require the attractive channel.")
#return e.real ?
return e
@cached_property
def C0(self):
r'''
The Wilson coefficient of the :math:`\mathcal{S}^0` piece of the potential.
'''
c0 = 0
for s in self.spheres:
if (0 == s.r).all() :
c0 += s.c
return c0