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

Lorenzo Cevolani (1) , Julien Despres (2, 3) , Giuseppe Carleo (4, 5) , Luca Tagliacozzo (6) , Laurent Sanchez-Palencia (2)

1 Institut für Theoretische Physik [Göttingen]
2 CPHT - Centre de Physique Théorique [Palaiseau]
3 Laboratoire Charles Fabry / Optique Quantique
4 ITP - Institute for Theoretical Physics [ETH Zürich]
5 Flatiron Institute
6 SUPA - Department of Physics

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

Mots clés: light-cone dynamics; quantum quench; long-range interactions; spreading of information

Domaines: Gaz Quantiques [cond-mat.quant-gas]; Matière Condensée [cond-mat]; Physique Quantique [quant-ph]

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. Physical Review B, 2018, 98 (2), ⟨10.1103/PhysRevB.98.024302⟩. ⟨hal-01532720v4⟩