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Let a general quantum many-body system at a low temperature adiabaticallycross through the vicinity of the system's quantum critical point. We show thatthe system's temperature is significantly suppressed due to both the entropymajorization theorem in quantum information science and the entropyconservation law in adiabatic processes. We take the one-dimensionaltransverse-field Ising model and spinless fermion system as concrete examplesto show that the inverse temperature might become divergent around theircritical points. Since the temperature is a measurable quantity in experiments,our work, therefore, provides a practicable proposal to detect quantum phasetransitions.

Entropy majorization, thermal adiabatic theorem, and quantum phase transitions