pyqula 0.0.4

Python library for quantum lattice tight binding models

SUMMARY

This is a Python library to compute quantum-lattice tight-binding models in different dimensionalities.

INSTALLATION

With pip (release version)

pip install pyqula

Manual installation (most recent version)

Clone the Github repository with

git clone https://github.com/joselado/pyqula

and add the "pyqula/src" path to your Python script with

import sys
sys.path.append(PATH_TO_PYQULA+"/src")

FUNCTIONALITIES

• Spinless, spinful and Nambu basis for orbitals
• Include magnetism, spin-orbit coupling and superconductivity
• Band structures and density of states
• Selfconsistent mean-field calculations with local/non-local interactions
• Topological characterization of electronic structures
• Green's function formalism for semi-infinite systems
• Spectral functions in infinite geometries
• Kernel polynomial based-methods
• Quantum Transport
• 0d, 1d, 2d and 3d tight binding models

EXAMPLES

A variety of examples can be found in pyqula/examples

Band structure of a honeycomb lattice

from pyqula import geometry
g = geometry.honeycomb_lattice() # get the geometry object
h = g.get_hamiltonian() # get the Hamiltonian object
h.get_bands() # compute the band structure

Mean field Hubbard model of a zigzag honeycomb ribbon

from pyqula import geometry
from pyqula import scftypes
g = geometry.honeycomb_zigzag_ribbon(10) # create geometry of a zigzag ribbon
h = g.get_hamiltonian() # create hamiltonian of the system
mf = scftypes.guess(h,"ferro",fun=lambda r: [0.,0.,1.])
scf = scftypes.hubbardscf(h,nkp=30,filling=0.5,mf=mf)
h = scf.hamiltonian # get the Hamiltonian
h.get_bands(operator="sz") # calculate band structure

Band structure of twisted bilayer graphene

from pyqula import specialgeometry
from pyqula.specialhopping import twisted_matrix
g = specialgeometry.twisted_bilayer(3)
h = g.get_hamiltonian(mgenerator=twisted_matrix(ti=0.12))
h.get_bands(nk=100)

Chern number of a Chern insulator

from pyqula import geometry
from pyqula import topology
g = geometry.honeycomb_lattice()
h = g.get_hamiltonian()
h.add_rashba(0.3) # Rashba spin-orbit coupling
h.add_zeeman([0.,0.,0.3]) # Zeeman field
c = topology.chern(h) # compute Chern number
print("Chern number is ",c)

Band structure of a nodal line semimetal

from pyqula import geometry
from pyqula import films
g = geometry.diamond_lattice_minimal()
g = films.geometry_film(g,nz=20)
h = g.get_hamiltonian()
h.get_bands()

Surface spectral function of the Haldane model

from pyqula import geometry
from pyqula import kdos
g = geometry.honeycomb_lattice()
h = g.get_hamiltonian()
h.add_haldane(0.05)
kdos.surface(h)

Antiferromagnet-superconductor interface

from pyqula import geometry
g = geometry.honeycomb_zigzag_ribbon(10) # create geometry of a zigzag ribbon
h = g.get_hamiltonian(has_spin=True) # create hamiltonian of the system
h.add_antiferromagnetism(lambda r: (r[1]>0)*0.5) # add antiferromagnetism
h.add_swave(lambda r: (r[1]<0)*0.3) # add superconductivity
h.get_bands() # calculate band structure

Fermi surface of a Kagome lattice

from pyqula import geometry
from pyqula import spectrum
import numpy as np
g = geometry.kagome_lattice()
h = g.get_hamiltonian()
spectrum.multi_fermi_surface(h,nk=60,energies=np.linspace(-4,4,100),
        delta=0.1,nsuper=1)