Spin dynamics of exotic quantum magnets

Stefan Wessel, Fakher Assaad


Quantum spin systems are an active, interesting area of current research on strongly-correlated quantum many-body systems, in particular as they provide an often well-defined platform to explore novel states of condensed matter, their corresponding excitations as well as quantum phase transitions that bound these phases to more conventional, magnetically ordered regions. Systems of interest include those that exhibit, e.g., quantum spin liquids, quantum-disordered phases, or spin nematic states. Furthermore, with refined experimental techniques, such as provided by neutron, light or x-ray scattering probes, it has become feasible to explore in addition to their thermodynamic properties also details of the excitations that emerge in such systems. The central goal of project P6 is to employ quantum Monte Carlo methods to provide reliable data for dynamical response functions for a wide range of quantum spin model systems that exhibit unconventional magnetic properties. In contrast to other numerical methods, which extract such dynamical information from the real-time dynamics, within quantum Monte Carlo simulations, equilibrium dynamical properties are accessible by measuring imaginary time-displaced correlation functions. In order to extract from the quantum Monte Carlo data the dynamical spectral function, an analytic continuation from the imaginary-time data to real frequencies is thus required. In the first grant period, we implemented and extended the algorithms to perform the spin dynamical measurements as well as the analytic continuation schemes. Furthermore, we already applied our methods to different two-dimensional spin systems. For the second grant period, we now plan to focus our quantum Monte Carlo simulations to calculate spectral functions that are relevant for scattering probes such as resonant inelastic x-ray scattering (RIXS) or infrared absorption spectroscopy. We plan in particular to consider spin chain and variable-width spin ladder systems, as well as two-dimensional magnetically ordered systems and sign-problem-free models of spin liquid phases. These studies will allow us to explore in detail the emergence
of e.g. magnon-bound states in such systems and provide unbiased reference data for advanced spectral probes of basic quantum magnetic model systems. Furthermore, we aim at extending our refined spectral probes to also explore the entanglement properties of quantum spin systems, based on recent advances in the numerical determination of the spectral properties of quantum-many-body entanglement Hamiltonians, where we can study both quantum critical points and unconventionally ordered and quantum disordered systems.