QuSpin: a Python package for dynamics and exact diagonalisation of quantum many body systems part I: spin chains

Abstract

We present a new open-source Python package for exact diagonalisation and quantum dynamics of spin(-photon) chains, called QuSpin, supporting the use of various symmetries in 1-dimension and (imaginary) time evolution for chains up to 32 sites in length. The package is well-suited to study, among others, quantum quenches at finite and infinite times, the Eigenstate Thermalisation hypothesis, many-body localisation and other dynamical phase transitions, periodically-driven (Floquet) systems, adiabatic and counter-diabatic ramps, and spin-photon interactions. Moreover, QuSpin's user-friendly interface can easily be used in combination with other Python packages which makes it amenable to a high-level customisation. We explain how to use QuSpin using four detailed examples: (i) Standard exact diagonalisation of XXZ chain (ii) adiabatic ramping of parameters in the many-body localised XXZ model, (iii) heating in the periodicallydriven transverse-field Ising model in a parallel field, and (iv) quantised light-atom interactions: recovering the periodically-driven atom in the semi-classical limit of a static Hamiltonian.

Treelike Interactions and Fast Scrambling with Cold Atoms

“…To verify that the s = 0 model is chaotic in the interacting quantum regime, we calculate the energy level statistics for a system of N = 16 sites at half filling by exact diagonalization [58]. Figure S3 shows the distribution of spacings between neighboring energy levels, after unfolding the spectrum in each momentum sector according to the procedure in Ref.…”

Does Scrambling Equal Chaos?

“…Acknowledgements.-It is a pleasure to thank Ehud Altman, Jorge Hirsch, Laimei Nie, and Daniel Parker for helpful discussions. Some of the quantum calculations have been performed using the QuSpin package [55,56] Appendix A: Saddle-dominated scrambling in Dicke model In this appendix, we show that saddle-dominated scrambling also takes place in the Dicke model [42,58]. Originally, it was conceived to describe N two-level atoms coupled to a single optical cavity mode.…”

Enhanced Superexchange in a Tilted Mott Insulator

“…We time-evolve the initial state either with no tilt ∆ = 0 or with a tilt tuned close to the resonance ∆ = 1.25. Calculations were performed using the open-source Python package for exact diagonalization and quantum dynamics QuSpin v0.3.2 [42,43].…”