Maximal steady-state entanglement and perfect thermal rectification in non-equilibrium interacting XXZ chains

We propose a scheme for dissipative preparation of maximal entanglement in a two-qubit Heisenberg XXZ model interacting asymmetrically with two independent boson thermal reservoirs with different temperature. One reservoir is common to both qubits, while the other is connected with just one qubit. We analytically and numerically investigate the steady-state entanglement of the qubits, based on the Markovian quantum master equation. We study the influence of the inherent asymmetry induced by the asymmetrically couplings of qubits to the reservoirs, on the steady-state entanglement of the qubits. While the temperature gradient of reservoirs generally deteriorate quantum correlations, we show that in the presence of the inherent asymmetry, the maximal entanglement can revive by increasing temperature gradient, at high base temperature of the reservoirs. We find that by turning on the asymmetry, perfect rectification can be achieved without introducing any additional asymmetry to the system. We also discover that the obtained perfect rectification is associated with maximizing of the steady-state entanglement.