Role of thermal field in entanglement harvesting between two accelerated Unruh-DeWitt detectors

We investigate the effects of field temperature $T^{(f)}$ on the entanglement harvesting between two uniformly accelerated detectors. For their parallel motion, the thermal nature of fields does not produce any entanglement, and therefore, the outcome is the same as the non-thermal situation. On the contrary, $T^{(f)}$ affects entanglement harvesting when the detectors are in anti-parallel motion, i.e., when detectors $A$ and $B$ are in the right and left Rindler wedges, respectively. While for $T^{(f)}=0$ entanglement harvesting is possible for all values of $A$'s acceleration $a_A$, in the presence of temperature, it is possible only within a narrow range of $a_A$. In $(1+1)$ dimensions, the range starts from specific values and extends to infinity, and as we increase $T^{(f)}$, the minimum required value of $a_A$ for entanglement harvesting increases. Moreover, above a critical value $a_A=a_c$ harvesting increases as we increase $T^{(f)}$, which is just opposite to the accelerations below it. There are several critical values in $(1+3)$ dimensions when they are in different accelerations. Contrary to the single range in $(1+1)$ dimensions, here harvesting is possible within several discrete ranges of $a_A$. Interestingly, for equal accelerations, one has a single critical point, with nature quite similar to $(1+1)$ dimensional results. We also discuss the dependence of mutual information among these detectors on $a_A$ and $T^{(f)}$.