It is shown that quantum corrections in acceleration calculated on the basis of the Zubarev density operator allow us to substantiate the
existence of the Unruh effect from the point of view of quantum statistical mechanics. A wide class of theories of free fields is
considered: real and complex scalar fields, Dirac field. Both massless and massive cases are investigated. In the case of bosonic fields,
infrared divergences arise; a consistent method for their regularization is proposed. The calculated corrections exactly correspond to
the quantum corrections to the vacuum value of the energy-momentum tensor in space-time with a conical singularity, such as cosmic
string. Thus, we establish the existence of exact duality between the Zubarev approach and the theory with a conical singularity, or the
existence of the emergent conical geometry in the approach with the density operator. A comparison of the corrections calculated by two
methods allows us to predict the absence of higher-order quantum corrections in acceleration in the chiral limit. In conclusion, the
effect associated with the existence of instability for accelerated medium at Unruh temperature is discussed.