Persistence of locality in systems with power-law interactions.

@article{Gong2014PersistenceOL,
  title={Persistence of locality in systems with power-law interactions.},
  author={Zhe-Xuan Gong and Michael Foss-Feig and Spyridon Michalakis and Alexey V. Gorshkov},
  journal={Physical review letters},
  year={2014},
  volume={113 3},
  pages={
          030602
        }
}
Motivated by recent experiments with ultracold matter, we derive a new bound on the propagation of information in D-dimensional lattice models exhibiting 1/r^{α} interactions with α>D. The bound contains two terms: One accounts for the short-ranged part of the interactions, giving rise to a bounded velocity and reflecting the persistence of locality out to intermediate distances, whereas the other contributes a power-law decay at longer distances. We demonstrate that these two contributions not… 

Figures from this paper

Dynamics of long-range interacting quantum spin systems
In this thesis we study the time evolution of correlation functions in quantum lattice models in the presence of long-range interactions or hopping decaying asymptotically as a power law. For a large
Emergent locality in systems with power-law interactions
TLDR
While the interactions are long-range, their effect on information spreading is asymptotically negligible as long as $\alpha>1$, which directly implies that all previously obtained rigorous bounds on information spread in long- range interacting systems are not tight, and thus could be improved.
Spreading of correlations in exactly-solvable quantum models with long-range interactions in arbitrary dimensions
We study the out-of-equilibrium dynamics induced by quantum quenches in quadratic Hamiltonians featuring both short- and long-range interactions. The spreading of correlations in the presence of
Interplay of Soundcone and Supersonic Propagation in Lattice Models with Power Law Interactions
We study the spreading of correlations and other physical quantities in quantum lattice models with interactions or hopping decaying like $r^{-\alpha}$ with the distance $r$. Our focus is on
Singular dynamics and emergence of nonlocality in long-range quantum models
We discuss how nonlocality originates in long-range quantum systems and how it affects their dynamics at and out of the equilibrium. We focus in particular on the Kitaev chains with long-range
Algebraic localization from power-law couplings in disordered quantum wires
We analyze the effects of disorder on the correlation functions of one-dimensional quantum models of fermions and spins with long-range interactions that decay with distance $\ell$ as a power-law
Exponentially slow heating in short and long-range interacting Floquet systems
We analyze the dynamics of periodically-driven (Floquet) Hamiltonians with short- and long-range interactions, finding clear evidence for a thermalization time, $\tau^*$, that increases exponentially
Locality and heating in periodically driven, power-law-interacting systems.
TLDR
It is conjecture that the gap between the results from the linear response theory and the Magnus-like expansion does not have physical implications, but is, rather, due to the lack of tight Lieb-Robinson bounds for power-law interactions.
Non-local propagation of correlations in quantum systems with long-range interactions
TLDR
This work applies a variable-range Ising spin chain Hamiltonian and aVariable-range XY spin chainHamiltonian to a far-from-equilibrium quantum many-body system and observes its time evolution, determining the spatial and time-dependent correlations, extracting the shape of the light cone and measuring the velocity with which correlations propagate through the system.
Origin of the slow growth of entanglement entropy in long-range interacting spin systems
Long-range interactions allow far-distance quantum correlations to build up very fast. Nevertheless, numerical simulations demonstrated a dramatic slowdown of entanglement entropy growth after a
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 90 REFERENCES
"J."
however (for it was the literal soul of the life of the Redeemer, John xv. io), is the peculiar token of fellowship with the Redeemer. That love to God (what is meant here is not God’s love to men)
Nature
  • R. Rosenfeld
  • Medicine
    Otolaryngology--head and neck surgery : official journal of American Academy of Otolaryngology-Head and Neck Surgery
  • 2009
疟原虫var基因转换速率变化导致抗原变异[英]/Paul H, Robert P, Christodoulou Z, et al//Proc Natl Acad Sci U S A
抗原变异可使得多种致病微生物易于逃避宿主免疫应答。表达在感染红细胞表面的恶性疟原虫红细胞表面蛋白1(PfPMP1)与感染红细胞、内皮细胞、树突状细胞以及胎盘的单个或多个受体作用,在黏附及免疫逃避中起关键的作用。每个单倍体基因组var基因家族编码约60种成员,通过启动转录不同的var基因变异体为抗原变异提供了分子基础。
Comm
  • Math. Phys. 265, 781
  • 2006
Commun
  • Math. Phys. 265, 781
  • 2006
Commun
  • Math. Phys. 28, 251
  • 1972
and C
  • Monroe, arXiv:1401.5088
  • 2014
and C
  • F. Roos, arXiv:1401.5387
  • 2014
PRL
  • PRL
  • 2014
and A
  • V. Gorshkov, (in preparation)
  • 2014
...
1
2
3
4
5
...