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Transport and spectral properties of the XX$+$XXZ diode and stability to dephasing

We study the transport and spectral property of a segmented diode formed by an XX $+$ XXZ spin chain. This system has been shown to become an ideal rectifier for spin current for large enough anisotropy. Here we show numerical evidence that the system in reverse bias has three different transport regimes depending on the value of the anisotropy: ballistic, diffusive and insulating. In forward bias we encounter two regimes, ballistic and diffusive. The system in forward and reverse bias shows significantly different spectral properties, with distribution of rapidities converging towards different functions. In the presence of dephasing the system becomes diffusive, rectification is significantly reduced, the relaxation gap increases and the spectral properties in forward and reverse bias tend to converge. For large dephasing the relaxation gap decreases again as a result of Quantum Zeno physics.