Anomalous spin entanglement in nonequilibrium systems

Abstract

Entanglement is an essential resource in quantum information science and it is often sensitive to temperature fluctuation. Quantifying and understanding the detailed influence of temperature on entanglement is important for both the fundamental interest and the application value. Here we theoretically study the entanglement distribution in a many-body system subjected to a temperature gradient and identify an entanglement difference on two sides of the system. This phenomenon is named the entanglement Seebeck effect, which is similar to the traditional Seebeck effect where an electric voltage can be generated on the two sides of a metal with different temperatures. (i) In contrast to general wisdom, the spins on the hotter side can have larger entanglement than those on the colder side of a magnetic system. This anomalous phenomenon is well explained by the increase of magnon density with the temperature in a magnetic system. (ii) The entanglement length (the critical distance beyond which the entanglement of electrons disappears) in such a nonequilibrium system is larger than that in an equilibrium system with equal temperature as a particular local temperature chosen from the nonequilibrium system. This enhancement is ascertained to result from the particle number fluctuation of a nonequilibrium state. Our findings provide a possible way to quantify the temperature influence on the spin entanglement in nonequilibrium many-body systems and may further benefit the experimental measurements of entanglement where the entanglement length is an important asset.