Phillip Weinberg

Adiabatic perturbation theory and geometry of periodically-driven systems

We give a systematic review of the adiabatic theorem and the leading non-adiabatic corrections in periodically-driven (Floquet) systems. These corrections have a two-fold origin: (i) conventional ones originating from the gradually changing Floquet Hamiltonian and (ii) corrections originating from changing the micro-motion operator. These corrections conspire to give a Hall-type linear response for non-stroboscopic (time-averaged) observables allowing one to measure the Berry curvature and the Chern number related to the Floquet Hamiltonian, thus extending these concepts to periodically-driven many-body systems. The non-zero Floquet Chern number allows one to realize a Thouless energy pump, where one can adiabatically add energy to the system in discrete units of the driving frequency. We discuss the validity of Floquet Adiabatic Perturbation Theory (FAPT) using five different models covering linear and non-linear few and many-particle systems. We argue that in interacting systems, even in the stable high-frequency regimes, FAPT breaks down at ultra slow ramp rates due to avoided crossings of photon resonances, not captured by the inverse-frequency expansion, leading to a counter-intuitive stronger heating at slower ramp rates. Nevertheless, large windows in the ramp rate are shown to exist for which the physics of interacting driven systems is well captured by FAPT.

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

We present a new open-source Python package for exact diagonalization 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, QuSpins 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 periodically-driven 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.