Entropy majorization, thermal adiabatic theorem, and quantum phase transitions

TL;DR

This paper demonstrates that during adiabatic crossing of quantum critical points, a system's temperature can be significantly suppressed or diverge, offering a practical way to detect quantum phase transitions.

Contribution

It connects entropy majorization and adiabatic laws to quantum critical phenomena, providing a new method to observe phase transitions through temperature measurements.

Findings

Temperature can be suppressed near critical points.

Inverse temperature may diverge at quantum critical points.

Proposes experimental detection of quantum phase transitions.

Abstract

Let a general quantum many-body system at a low temperature adiabatically cross through the vicinity of the system's quantum critical point. We show that the system's temperature is significantly suppressed due to both the entropy majorization theorem in quantum information science and the entropy conservation law in adiabatic processes. We take the one-dimensional transverse-field Ising model and spinless fermion system as concrete examples to show that the inverse temperature might become divergent around their critical points. Since the temperature is a measurable quantity in experiments, our work, therefore, provides a practicable proposal to detect quantum phase transitions.