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Effect of Phonons and Impurities on the Quantum Transport in XXZ Spin-Chains

Numerical and analytic results have been used to characterize quantum transport in spin chains, showing the existence of both ballistic and diffusive motion. Experiments have shown that heat transfer is surprisingly always diffusive. The scattering from phonons and impurities have been postulated to be the two factors critical in causing the diffusive transport. In this work, we evaluate the transport process by incorporating a bath of phonons and impurities in order to understand the role played by each of the factors. While methods like time-dependent density matrix renormalization group (tDMRG) can be used to simulate isolated spin chains, the coupling with phonons make simulations significantly more challenging. The recently developed multisite tensor network path integral (MS-TNPI) method builds a framework for simulating the dynamics in extended open quantum systems by combining ideas from tDMRG and Feynman-Vernon influence functional. This MS-TNPI is used to characterize dynamics in open, extended quantum systems. Simulations are done with the commonly used sub-Ohmic, Ohmic and super-Ohmic spectral densities describing the phononic bath. We show that while the transport in presence of impurities eventually becomes diffusive, the exact details are dependent on the specifics of the interactions and amount of impurities. In contrast, the presence of a bath makes the transport diffusive irrespective of the parameters characterizing the bath.