• Corpus ID: 209202484

Absence of temporal order in states with spatial correlation decay

@article{Huang2019AbsenceOT,
  title={Absence of temporal order in states with spatial correlation decay},
  author={Yichen Huang},
  journal={arXiv: Statistical Mechanics},
  year={2019}
}
  • Yichen Huang
  • Published 3 December 2019
  • Physics
  • arXiv: Statistical Mechanics
In quantum lattice systems, we prove that any stationary state with power-law (or even exponential) decay of spatial correlations has vanishing macroscopic temporal order in the thermodynamic limit. Assuming translational invariance, we obtain a similar bound on the temporal order between local operators at late times. Our proofs do not require any locality of the Hamiltonian. Applications in quantum time crystals are briefly discussed. 
Reply to "Comment on "Quantum Time Crystals from Hamiltonians with Long-Range Interactions""
In the note by Khemani et al. [arXiv:2001.11037] the authors express conceptual disagreement with our recent paper on quantum time crystals [Phys. Rev. Lett. 123, 210602]. They criticise the

References

SHOWING 1-10 OF 16 REFERENCES
Proof of the Absence of Long-Range Temporal Orders in Gibbs States
We address the question whether time translation symmetry can be spontaneously broken in a quantum many-body system. One way of detecting such a symmetry breaking is to examine the time-dependence of
Locality of temperature
This work is concerned with thermal quantum states of Hamiltonians on spin and fermionic lattice systems with short range interactions. We provide results leading to a local definition of
Gibbs states of a one dimensional quantum lattice
A one dimensional infinite quantum spin lattice with a finite range interaction is studied. The Gibbs state in the infinite volume limit is shown to exist as a primary state of a UHF algebra. The
Time Evolution of Correlation Functions in Quantum Many-Body Systems.
TLDR
It is shown that in a large class of translation-invariant models the correlation functions factorize at late times, thus proving that dissipation emerges out of the unitary dynamics of the system, and an upper bound on the timescale at which they reach the factorized late time value is provided.
Quantum Time Crystals from Hamiltonians with Long-Range Interactions.
TLDR
This study proposes a form of a Hamiltonian for which the unitary dynamics exhibits the time crystalline behavior and breaks continuous TTS, based on a spin-1/2 many-body Hamiltonian which has long-range multispin interactions in the form of spin strings, thus bypassing previously known no-go theorems.
Finite-Size Scaling of Out-of-Time-Ordered Correlators at Late Times.
TLDR
It is shown that the residual value of the out-of-time-ordered correlator of generic traceless local operators can provide useful insights into the chaotic dynamics of quantum many-body systems.
Absence of Quantum Time Crystals.
TLDR
A no-go theorem is proved that rules out the possibility of time crystals defined as such, in the ground state or in the canonical ensemble of a general Hamiltonian, which consists of not-too-long-range interactions.
Discrete Time Crystals
Experimental advances have allowed for the exploration of nearly isolated quantum many-body systems whose coupling to an external bath is very weak. A particularly interesting class of such systems
Spectral Gap and Exponential Decay of Correlations
We study the relation between the spectral gap above the ground state and the decay of the correlations in the ground state in quantum spin and fermion systems with short-range interactions on a wide
A bound on chaos
A bstractWe conjecture a sharp bound on the rate of growth of chaos in thermal quantum systems with a large number of degrees of freedom. Chaos can be diagnosed using an out-of-time-order correlation
...
1
2
...