Nonexistence of spontaneous symmetry breakdown of time-translation symmetry on general quantum systems: Any macroscopic order parameter moves not!

TL;DR

This paper reviews the fundamental impossibility of genuine quantum time crystals in general quantum systems, based on the KMS condition, which prevents spontaneous time-translation symmetry breaking in equilibrium states.

Contribution

It clarifies that genuine quantum time crystals cannot exist in equilibrium due to the KMS condition, reaffirming known results since the 1970s.

Findings

Spontaneous time-translation symmetry breaking is impossible in quantum systems.

Genuine quantum time crystals are excluded in equilibrium states.

Non-trivial temporal orders cannot exist in equilibrium quantum systems.

Abstract

This review informs that the impossibility of genuine quantum time crystals has been known in the C*-algebraic quantum statistical mechanics since 1970s. The KMS condition implies that spontaneous breakdown of time-translation symmetry is impossible in general quantum systems. In particular, any non-trivial order, such as periodic, quasi-periodic, and chaotic order cannot exist in the time direction of equilibrium states, meaning that genuine quantum time crystals are excluded from the outset.