pyqula 0.0.1

Python library for tight binding model

SUMMARY

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

CAPABILITIES

• 0d, 1d, 2d and 3d systems
• Band structures
• Density of states
• Include magnetism, spin-orbit coupling and superconductivity
• Selfconsistent mean-field calculations with local/non-local interactions
• Topological characterization of electronic structures
• Green's function formalism for semi-infinite systems
• Spectral functions
• Kernel polynomial techniques
• Quantum Transport

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)

INSTALLATION

With pip (release version)

pip install pyqula-joselado

Manual installation (most recent version)

Clone this repository with

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

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

import sys
sys.path.append(PATH_TO_PYQULA)

Parts of the code are written in Fortran for a matter of performance. To compile those functions you need to execute "install.sh" In case they are not compiled, the library will still work but certain parts will be substantially slower. Compiling the fortran routines requires having a fortran compiler, such as gfortran.

Parts of the code rely on Python libraries

• numpy
• scipy
• multiprocess
• numba