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Absence of Quantum Time Crystals
Haruki Watanabe1, Masaki Oshikawa2
1Department of Physics, University of California, Berkeley, California 94720, USA.
Physical Review Letters
|July 22, 2015
Summary
Researchers explored the concept of time crystals, phases breaking continuous time translation. A new definition was proposed, leading to a theorem showing time crystals are impossible in general Hamiltonian systems.
Area of Science:
- Condensed matter physics
- Quantum mechanics
- Statistical mechanics
Background:
- The concept of time crystals, analogous to spatial crystals, was recently proposed.
- Time crystals represent phases that spontaneously break continuous time translation symmetry.
- The physical realization of time crystals has been a subject of intense theoretical debate.
Purpose of the Study:
- To establish a precise definition for time crystals.
- To investigate the possibility of realizing time crystals in physical systems.
- To resolve the ongoing debate regarding the existence of time crystals.
Main Methods:
- Definition of time crystals based on time-dependent correlation functions of the order parameter.
- Development of a no-go theorem applicable to general Hamiltonian systems.
- Analysis of systems in the ground state and canonical ensemble.
Main Results:
- A rigorous definition of time crystals was formulated.
- A no-go theorem was proven, demonstrating the impossibility of time crystals under general conditions.
- The theorem applies to systems with not-too-long-range interactions.
Conclusions:
- Time crystals, as defined, cannot exist in the ground state or canonical ensemble of general Hamiltonian systems.
- The findings resolve a significant debate in condensed matter physics.
- Further theoretical and experimental work may be needed to explore alternative definitions or related phenomena.
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