This program allows to perform tight binding calculations with a user friendly interface in a variety of lattices and dimensionalities.

Here you can see four simultaneous examples of the usage of Quantum Lattice.

Below you can see videos showing the real-time usage of this program for individual examples

• Confined modes in graphene nanoislands
• Superlattices
• Interaction-induced magnetism
• Artificial Chern insulators
• Landau levels and quantum Hall edge states
• Twisted bilayer graphene

The program runs in Linux and Mac machines.

Clone the GitHub repository

git clone https://github.com/joselado/quantum-lattice

and execute the script install as

python install.py

The script will install all the required dependencies if they are not already present for the python command used. Afterwards, you can run the program by executing in a terminal

quantum-lattice

You can see here a short video demonstrating the installation.

For using this program in Windows, the easiest solution is to create a virtual machine using Virtual Box, installing a version of Ubuntu in that virtual machine, and following the previous instructions.

• 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

• 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
• Automatic identification of order parameters for symmetry broken states

• Berry phases, Berry curvatures, Chern numbers and Z2 invariants
• Operator-resolved Chern numbers and Berry density

• Surface spectral functions for semi-infinite systems
• Single impurities in infinite systems
• Operator-resolved spectral functions

• Local and full spectral functions
• Operator resolved spectral functions
• Reaching system sizes up to 1000000 atoms on a single-core laptop

Quantum Lattice uses pyqula.

Electronic band structure, Berry curvature and momentum resolved surface spectral function of a px + ipy spin-triplet topological superconductor with d-vector (0,0,1).

Electronic band structure and selfconsistent local magnetization of a square lattice with an applied Zeeman field and local Hubbard interactions.

Electronic band structure, Fermi surface and local density of states of a superlattice built from a defective triangular lattice

Real space simulation of the STS spectra, using atomic-like orbitals for a nanographene island

Fermi surface and band structure of a two-dimensional lattice, including both first and second neighbor hoppings. In the absence of second neighbor hopping, the lowest band is flat. Only first neighbor hoppings are shown in the 3D structure plot.

Non-interacting and interacting band structure of a two-dimensional Lieb lattice. When repulsive local Hubbard interactions are included, an spontaneously ferromagnetic state appears in the system, leading to a real-space magnetic distribution.

Kagome lattice with Rashba spin-orbit coupling and exchange field, giving rise to a net Chern number and chiral edge states

Honeycomb lattice with Kane-Mele spin-orbit coupling and Rashba spin-orbit coupling, giving rise to a gapped spectra with a non-trivial Z2 invariant and helical edge states https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.226801

Self-consistent mean field calculation of a zigzag graphene ribbon, with electronic interactions included as a mean field Hubbard model. Interactions give rise to an edge magnetization in the ribbon, with an antiferromagnetic alignment between edges

Three-dimensional quantum spin-Hall insulator, engineered by intrinsic spin-orbit coupling in the diamond lattice. the top and bottom of the slab show an emergent helical electron gas.

Real space simulation of the STS spectra, using atomic-like orbitals for a graphene nanoribbon

Band structure of a slab of a 3D nodal line semimetal in a diamond lattice, showing the emergence of topological zero energy drumhead states in the surface of the slab https://link.springer.com/article/10.1007%2Fs10909-017-1846-3

Spectra and spatially resolved density of states of square quantum dot, showing the emergence of confined modes

Density of states and spatially resolved density of states of a big graphene quantum dot. The huge islands module uses special techniques to efficiently solve systems with hundreds of thousands of atoms.

Electronic spectra of a graphene lattice in the presence of an off-plane magnetic field and antiferromagnetic order, giving rise to Landau levels and chiral edge states

Bogoliuvov de Gennes band structure of a two-dimensional gas in a square lattice with Rashba spin-orbit coupling, off-plane exchange field and s-wave superconducting proximity effect. When superconductivity is turned on, a gap opens up in the spectra hosting a non-trivial Chern number, giving rise to propagating Majorana modes in the system

Band structure of Bernal stacked bilayer graphene, showing the emergence of a gap when an interlayer bias is applied. The previous gap hosts a non-trivial valley Chern number, giving rise to the emergence of pseudo-helical states in the edge of the system

Bandstructure and Fermi surface of a twisted graphene bilayer, showing the emergence of nearly flat bands https://journals.aps.org/prb/abstract/10.1103/PhysRevB.82.121407

Structure and band structure of a twisted graphene trilayer at the magic angle.