Python library to perform quantics tensor cross interpolation. The library is built on top of QuanticsTCI.jl and xfacpy
The folder examples contains several use cases of the library
Some of the examples use the library for electronic structure pyqula
Below you can see a minimal example of a mean field calculation using the quantics tensor cross interpolation algorithm combined with the kernel polynomial method for an interacting Hubbard Hamiltonian.
from qtcipy.tbscftk import hamiltonians
import numpy as np
L = 12 # exponential length, leads to 2**L sites
H = hamiltonians.chain(L) # get the Hamiltonian
def f(r):
"""Modulation of the hopping"""
omega = np.pi*2.*np.sqrt(2.)/(2**L/10) # frequency of the modulation
return 1. + 0.2*np.cos(omega*r[0]) # return correction to the hopping
H.modify_hopping(f) # modify the hopping
SCF = H.get_SCF_Hubbard(U=3.0) # generate a selfconsistent object
SCF.solve(use_qtci=True,use_kpm=True)
Mz = SCF.Mz # selfconsistent magnetizationThe moire Hamiltonian and resulting selfconsistent electronic order are
We will now see how an interface between two moire patterns can be computed
from qtcipy.tbscftk import hamiltonians
import numpy as np
L = 14 # exponential length, leads to 2**L sites
H = hamiltonians.chain(L) # get the Hamiltonian
def f(r):
"""Modulation of the hopping"""
omega1 = np.pi*2.*np.sqrt(2.)/(2**L/10) # left frequency
omega2 = np.sqrt(3)*omega1 # right frequency
if r[0]<0.: return 0.2*np.sin(omega1*r[0]) # return correction to the hopping
else: return 0.1*np.sin(omega2*r[0]) # return correction to the hopping
H.modify_hopping(f) # modify the hopping
SCF = H.get_SCF_Hubbard(U=3.0) # generate a selfconsistent object
SCF.solve(use_qtci=True,use_kpm=True)
Mz = SCF.Mz # selfconsistent magnetizationThe moire Hamiltonian and resulting selfconsistent electronic order are
We will now compute a moire pattern with non-uniform strain
from qtcipy.tbscftk import hamiltonians
import numpy as np
L = 16 # exponential length, leads to 2**L sites
H = hamiltonians.chain(L) # get the Hamiltonian
def f(r):
"""Modulation of the hopping"""
length = 2**L # total length
omega0 = np.pi*2.*np.sqrt(2.)/(length/20) # base frequency
omega = omega0*(1 + r[0]/length) # position-dependent frequency
return 0.2*np.sin(omega*r[0]) # return correction to the hopping
H.modify_hopping(f) # modify the hopping
SCF = H.get_SCF_Hubbard(U=3.0) # generate a selfconsistent object
SCF.solve(use_qtci=True,use_kpm=True)
Mz = SCF.Mz # selfconsistent magnetizationThe moire Hamiltonian and resulting selfconsistent electronic order are
Documentation about the kernel polynomial tensor cross interpolation algorithm for interacting tight binding models can be found here
You can find a detailed discussion about the kernel polynomial tensor cross interpolation algorithm for large interacting tight binding models in arXiv:2409.18898
You need to have Julia installed in your computer. Afterwards, execute "python install.py" in the current directory. Julia needs to be in your PATH, as the code will use the output of "which julia"
If you want to install the C++ version, use
python install_cpp.pyFor the kernel polynomial quantics tensor cross algorithm for interacting tight binding models, the library pyqula has to be installed
pip install pyqula