Universal Scaling Laws for Correlation Spreading in Quantum Systems with Short- and Long-Range Interactions - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2018

Universal Scaling Laws for Correlation Spreading in Quantum Systems with Short- and Long-Range Interactions

Résumé

We study the spreading of information in a wide class of quantum systems, with variable-range interactions. We show that, after a quench, it generally features a double structure, whose scaling laws are related to a set of universal microscopic exponents that we determine. When the system supports excitations with a finite maximum velocity, the spreading shows a twofold ballistic behavior. While the correlation edge spreads with a velocity equal to twice the maximum group velocity, the dominant correlation maxima propagate with a different velocity that we derive. When the maximum group velocity diverges, as realizable with long-range interactions, the correlation edge features a slower-than-ballistic motion. The motion of the maxima is, instead, either faster-than-ballistic, for gapless systems, or ballistic, for gapped systems. The phenomenology that we unveil here provides a unified framework, which encompasses existing experimental observations with ul-tracold atoms and ions. It also paves the way to simple extensions of those experiments to observe the structures we describe in their full generality. Introduction. – The ability of a quantum system to establish long-distance correlations and entanglement, as well as mutual equilibrium between distant parts, is determined by the speed at which information can propagate throughout the system. For lattice models with short-range interactions, Lieb and Robinson have demonstrated the existence of a maximum propagation speed limit, even for non-relativistic theories. This bound sets a linear causality cone beyond which correlations decay exponentially [1]. In a large class of many-body systems the information is carried by quasi-particles and the cone velocity may be related to their maximum velocity [2, 3], whenever it exists. Ballistic propagation of quantum correlations has received experimental [4, 5] and numerical [6–8] assessment, with, however, a cone velocity that may significantly differ from that expected. For long-range interactions, a different form of causal-ity arise due to direct coupling between local observables at arbitrary long distances. Long-range interactions appear in a variety of contexts, including van der Waals interactions Rydberg atom gases [9–12], effective photon-photon interactions in nonlinear media [13], dipole-dipole interactions between polar molecules [14–16] and magnetic atoms [17–21], photon-mediated interactions in su-perconductors [22] and artificial ion crystal [23–27], and solid-state defects [28–30]. They can be modelled by couplings decaying algebraically, 1/R α , with the distance R. For such systems, known extensions of the Lieb-Robinson (LR) bound in D dimensions include a logarithmic bound, t ∼ log(R), for α > D [31] and an algebraic bound, t ∼ R β with β < 1, for α > 2D [32]. In both cases, they are super-ballistic. No bound is known
Fichier principal
Vignette du fichier
paper20171222.pdf (987.69 Ko) Télécharger le fichier
LRTI_MAXIMA.pdf (13.22 Ko) Télécharger le fichier
MaximaXY2.pdf (13.67 Ko) Télécharger le fichier
PY_LRTI_Epsilon.pdf (22.18 Ko) Télécharger le fichier
PY_LRXY_EPSILON.pdf (74.17 Ko) Télécharger le fichier
mergeFig1.pdf (146.88 Ko) Télécharger le fichier
mergeFig2.pdf (279.3 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)
Origine Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-01532720 , version 1 (02-06-2017)
hal-01532720 , version 2 (12-06-2017)
hal-01532720 , version 3 (25-04-2018)
hal-01532720 , version 4 (09-07-2018)

Licence

Identifiants

  • HAL Id : hal-01532720 , version 3

Citer

Lorenzo Cevolani, Julien Despres, Giuseppe Carleo, Luca Tagliacozzo, Laurent Sanchez-Palencia. Universal Scaling Laws for Correlation Spreading in Quantum Systems with Short- and Long-Range Interactions. 2018. ⟨hal-01532720v3⟩
587 Consultations
431 Téléchargements

Partager

Gmail Mastodon Facebook X LinkedIn More