Examples¶

For a detailed tutorial on how to use the package, check out these papers:

• SciPost Phys. 2, 003 (2017).

• SciPost Phys. 7, 020 (2019).

The following Python scripts demonstrate basic and advanced functionality of QuSpin. In many cases, we have chosen to exhibit QuSpin’s functionality, and there may exist a more efficient approach to obtain the same result using QuSpin.

To run the example scripts, besides QuSpin, you have to also install matplotlib (e.g. by using anaconda):

• Getting started

  • Basics of QuSpin basis objects, download script

  • Exact Diagonalisation of Spin Hamiltonians, download script

  • User-defined ODEs: the Gross-Pitaevskii Equation and Nonlinear Time Evolution, download script

• Parallel computing in QuSpin

  • Parallel Computing in QuSpin, download script

• Basic usage

  • non-interacting systems

    • Free Particle Systems: the Fermionic SSH Chain, download script

    • Quantised Light-Atom Interactions in the Semi-classical Limit: Recovering the Periodically Driven Atom, download script

    • Optical Bloch equations: Lindblad dynamics using the matvec function, download script

    • The Spectrum of the Transverse Field Ising Model and the Jordan-Wigner Transformation, download script

  • interacting systems

    • Fermi-Hubbard model without doubly-occupied sites, download script

    • Hexagonal Lattice: Fermi-Hubbard model [courtesy of A. Buyskikh], download script

    • Heating in Periodically Driven Spin Chains, download script

    • The Bose-Hubbard Model on Translationally Invariant Ladder, download script

    • Integrability Breaking and Thermalising Dynamics in the 2D Transverse-Field Ising Model, download script

    • Many-Body Localization in the Fermi-Hubbard Model, download script

    • Adiabatic Control of Parameters in Many-Body Localised Phases, download script

    • Out-of-Equilibrium Bose-Fermi Mixtures, download script

    • Majorana Fermions: SYK Model, download script

• Advanced usage

  • Quantum scars Hamiltonian: spin-1/2 system with Hilbert space constraint, download script

  • Spin-1/2 system with sublattice particle consevation, download script

  • Applying symmetries to reduce user-imported bases using QuSpin, download script

  • Autocorrelation functions using symmetries, download script

  • Direct Calculation of spectral functions using symmetries, download script

  • Gell-Mann Operators for Spin-1 systems, download script

  • Majorana Fermions: Spinless Fermi-Hubbard Model, download script

  • NEW: Kitaev’s honeycomb Hamiltonian in vortex sectors given by the plaquette operators, download script

• Algorithms and Routines

  • Monte Carlo Sampling Expectation Values of Obsevables, download script

  • Efficient time evolution using the omp-parallelized expm_multiply_parallel, download script

  • Lanczos module: time-evolution and ground state search, download script

  • Lanczos module: finite-temperature calculations, download script

  • NEW: Liouville-von Neumann Equation using the MKL-enhanced Sparse Matrix Product [courtesy of J. Verlage], download script

Tutorials¶

We also have a small number of tutorials in Jupyter notebook format:

• Bose Hubbard Model, download ipynb, download script

• Fermi Hubbard Model, download ipynb, download script

• Su Schrieffer Heeger Model, download ipynb, download script

• Gross Pitaevskii Equation, download ipynb, download script