Nonexistence of spontaneous symmetry breakdown of time-translation symmetry on general quantum systems: Any macroscopic order parameter moves not!
arXiv:2201.06051 · doi:10.1142/S0129055X2330008X
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.
arXiv commentThis is a review paper to be published in Reviews in Mathematical Physics
References in corpus (20)
- Observation of a Discrete Time Crystal
- Observation of discrete time-crystalline order in a disordered dipolar many-body system
- Quantum Time Crystals
- Time crystals: a review
- Absence of Quantum Time Crystals
- Observation of Time-Crystalline Eigenstate Order on a Quantum Processor
- Impossibility of Spontaneously Rotating Time-Crystals: A No-Go Theorem
- Observation of time quasicrystal and its transition to superfluid time crystal
- Space-time crystals of trapped ions
- Comment on "Quantum Time Crystals": a new paradigm or just another proposal of perpetuum mobile?
- Quantum Time Crystals from Hamiltonians with Long-Range Interactions
- Symmetry Breaking and Finite Size Effects in Quantum Many-Body Systems
- Time crystal platform: from quasi-crystal structures in time to systems with exotic interactions
- Comment on "Space-Time Crystals of Trapped Ions": And Yet it Moves Not !
- On the broken time translation symmetry in macroscopic systems: precessing states and off-diagonal long-range order
- Proof of the absence of long-range temporal orders in Gibbs states
- Quantum Time Crystal By Decoherence: Proposal With Incommensurate Charge Density Wave Ring
- A Decade of Time Crystals: Quo Vadis?
- Examples of DLR states which are not weak limits of finite volume Gibbs measures with deterministic boundary conditions
- Macroscopic Dynamics of the Strong-Coupling BCS-Hubbard Model