Anti-Unruh effect in the thermal background

We study the influence of the thermal background on the existence of the anti-Unruh effect. For the massless scalar field, we present that the anti-Unruh effect can appear when the detector is accelerated in the thermal field, which is shown to be absent when accelerating in the Minkowski vacuum. For the massive scalar field, it is found that the anti-Unruh effect which exists in the case for accelerated detectors in the vacuum can disappear when the background temperature increases. We use the many-body entangled quantum state to study the situation of the massive scalar field. When the many-body state is accelerated, its entanglement is decreasing with the increase of the background temperature and the phenomenon of the sudden death for entanglement occurs. This provides a valuable indication that the anti-Unruh effect can exist below some specific background temperature, dependent on the actual experimental environment.