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

TL;DR

This paper investigates how phonons and impurities influence quantum transport in XXZ spin chains, revealing that impurities cause diffusive behavior depending on interactions, while phononic baths induce diffusion regardless of their specific properties.

Contribution

The study introduces the MS-TNPI method to simulate open quantum systems with phonons and impurities, providing new insights into their roles in quantum transport.

Findings

Impurities lead to diffusive transport depending on interaction details.

Phononic baths induce diffusive transport regardless of spectral density.

Transport becomes diffusive in the presence of a phononic bath.

Abstract

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.