Entropy majorization, thermal adiabatic theorem, and quantum phase transitions

2009/08/26 by Shi-Jian Gu, Gu, Shi-Jian
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech) #Strongly Correlated Electrons (cond-mat.str-el) #cond-mat.stat-mech #cond-mat.str-el

paper · pdf · doi:10.48550/arxiv.0908.3783

8 pages, 4 figures, submit to PRE

arxiv created 2009/08/26 · openalex publication_date 2009/08/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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