pyqula 0.0.22

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

Single particle Hamiltonians

• Spinless, spinful and Nambu basis for orbitals
• Full non-collinear electron and Nambu formalism
• Include magnetism, spin-orbit coupling and superconductivity
• Band structures with state-resolved expectation values
• Momentum-resolved spectral functions
• Local and full operator-resolved density of states
• 0d, 1d, 2d and 3d tight binding models
• Electronic structure unfolding in supercells

Interacting mean-field Hamiltonians

• Selfconsistent mean-field calculations with local/non-local interactions
• Both collinear and non-collinear formalism
• Anomalous mean-field for non-collinear superconductors
• Full selfconsistency with all Wick terms for non-collinear superconductors
• Constrained and unconstrained mean-field calculations
• Automatic identification of order parameters for symmetry broken states

Topological characterization

• Berry phases, Berry curvatures, Chern numbers and Z2 invariants
• Operator-resolved Chern numbers and Berry density
• Frequency resolved topological density
• Spatially resolved topological flux
• Real-space Chern density for amorphous systems
• Wilson loop and Green's function formalism

Spectral functions

• Spectral functions in infinite geometries
• Surface spectral functions for semi-infinite systems
• Interfacial spectral function in semi-infinite junctions
• Single impurities in infinite systems
• Operator-resolved spectral functions
• Green's function renormalization algorithm

Chebyshev kernel polynomial based-algorithms

• Local and full spectral functions
• Non-local correlators and Green's functions
• Locally resolved expectation values
• Operator resolved spectral functions
• Reaching system sizes up to 10000000 atoms on a single-core laptop

Quantum transport

• Metal-metal transport
• Metal-superconductor transport
• Fully non-collinear Nambu basis
• Non-equilibrium Green's function formalism
• Operator-resolved transport
• Differential decay rate
• Tunneling and contact scanning probe spectroscopy

EXAMPLES

A variety of examples can be found in pyqula/examples

Band structure of a Kagome lattice

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

Valley-resolved band structure of a honeycomb superlattice

from pyqula import geometry
g = geometry.honeycomb_lattice() # get the geometry object
g = g.get_supercell(2) # create a supercell
h = g.get_hamiltonian() # get the Hamiltonian object
(k,e,v) = h.get_bands(operator="valley") # compute the band structure

Non-unitarity of an interacting spin-triplet superconductor

from pyqula import geometry
g = geometry.triangular_lattice() # generate the geometry
h = g.get_hamiltonian() # create Hamiltonian of the system
h.add_exchange([3.,3.,3.]) # add exchange field
h.setup_nambu_spinor() # initialize the Nambu basis
# perform a superconducting non-collinear mean-field calculation
h = h.get_mean_field_hamiltonian(V1=-1.0,filling=0.3,mf="random")
# compute the non-unitarity of the spin-triplet superconducting d-vector
d = h.get_dvector_non_unitarity() # non-unitarity of spin-triplet

Mean-field with local interactions of a zigzag honeycomb ribbon

from pyqula import geometry
g = geometry.honeycomb_zigzag_ribbon(10) # create geometry of a zigzag ribbon
h = g.get_hamiltonian() # create hamiltonian of the system
h = h.get_mean_field_hamiltonian(U=1.0,filling=0.5,mf="ferro")
(k,e) = h.get_bands(operator="sz") # calculate band structure

Band structure of twisted bilayer graphene

from pyqula import specialhamiltonian # special Hamiltonians library
h = specialhamiltonian.twisted_bilayer_graphene() # TBG Hamiltonian
(k,e) = h.get_bands() # compute band structure

Chern number of a Chern insulator

from pyqula import geometry
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 = h.get_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()
(k,e) = h.get_bands()

Surface spectral function of a Chern insulator

from pyqula import geometry
from pyqula import kdos
g = geometry.honeycomb_lattice() # create honeycomb lattice
h = g.get_hamiltonian() # create hamiltonian of the system
h.add_haldane(0.05) # Add Haldane coupling
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
(k,e) = 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() # create geometry of the system
h = g.get_hamiltonian() # create hamiltonian of the system
spectrum.multi_fermi_surface(h,nk=60,energies=np.linspace(-4,4,100),
        delta=0.1,nsuper=1)