Finite-Temperature Dynamics with Matrix Product State and Cluster Approaches

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A variety of experimental probes is available for the investigation of dynamic susceptibilities. By indicating the allowed excitations of a system, these quantities often permit us to establish the properties of the quantum state. To do so, we however also need theoretical access to the spectra of appropriate effective low-energy models. The present proposal aims at extending the range of available numerical tools for this task. In particular, we plan to address finite temperatures in order to investigate signatures of ordered phases as opposed to disordered high-temperature states. Matrix Product State approaches (MPS) and cluster techniques like the Cluster Perturbation Theory (CPT) and the Variational Cluster Approximation (VCA) can be used to treat strongly correlated quantum systems at finite temperatures, but have so far mostly been applied to the ground state at T = 0. In this project, we plan to extend the range of applicability of both methods to treat spin and electron systems at finite temperatures in two-dimensional (2D) and quasi-2D geometries, to compare their predictive power, and to use MPS approaches at finite temperature as cluster solver. This will lead to cluster methods for 2D systems working at finite temperature and being more reliable since the results will be based on larger clusters. In particular we plan to focus on finite-temperature dynamical spectral functions, which are directly accessible via experiments like, e.g., neutron scattering, angle-resolved photo-electron spectroscopy (ARPES) or resonant inelastic X-ray scattering (RIXS). The goal is to predict signatures expected for spin or electron systems (e.g., iridate systems) in topologically nontrivial phases and to investigate them as they go through phase transitions from trivial to nontrivial states.