Universal scaling laws for correlation spreading in quantum systems with short- and long-range interactions

Abstract

The spreading of correlations after a quantum quench is studied in a wide class of lattice systems, with short-and long-range interactions. Using a unifying quasi-particle framework, we unveil a rich structure of the correlation cone, which encodes the footprints of several microscopic properties of the system. When the quasi-particle excitations propagate with a bounded group velocity, we show that the correlation edge and correlation maxima move with different velocities that we derive. For systems with a divergent group velocity, especially relevant for long-range interacting systems, the correlation edge propagates slower than ballistic. In contrast, the correlation maxima propagate faster than ballistic in gapless systems but ballistic in gapped systems. Our results shed new light on existing experimental and numerical observations, and pave the way to the next generation of experiments. For instance, we argue that the dynamics of correlation maxima can be used as a witness of the elementary excitations of the system. arXiv:1706.00838v3 [cond-mat.stat-mech]

The connection between holographic entanglement and complexity of purification

“…By calculating butterfly velocities and scrambling times [42][43][44], one could then study holographically how the information and with what "speed" could flow between the regions A and B along the surface Γ, or rather far from it into the bulk and in the region D. Therefore, a new characteristic time similar to the scrambling time, would be defined using this measure. Also both EoP and CoP would be implemented to probe various phase important transitions such as phases interpolating between Mott insulator and superfluid phase [41]. We leave these explorations to our upcoming works.…”

Emergent locality in systems with power-law interactions

“…Interestingly this question was not addressed directly by considering C x (t) . Instead, previous studies considered spatial one-time correlation functions, K x (t) ≡ Tr ρ 0 (t)Â iBi+x , whereρ 0 was taken to be either some special state [31][32][33] or a state resulting from a quench from the groundstate [33][34][35][36][37][38][39][40][41] (c.f. Ref.…”

“…To answer this question, one must consider generic long-range systems. Spreading of K x (t) correlations in such systems were studied using numerically exact methods [31,33,34,46], variational methods [35] and by approximately reducing them to quadratic effective models, either by studying the corresponding quasiparticle descriptions [35,36,40,41], by restrictions to the one-particle sector [32], or by using renormalization group techniques [37]. These studies suggest nonuniversal behavior, which depends both on the model but also on the initial condition.…”

Twofold correlation spreading in a strongly correlated lattice Bose gas

“…For lattice systems with local interactions, the existence of Lieb-Robinson (LR) bounds implies the emergence of a causal light cone beyond which the correlations are exponentially suppressed [6][7][8]. So far, light-cone-like spreading of correlations has been reported in short-range interacting models [9][10][11][12] as well as long-range models [13][14][15][16][17][18][19][20][21][22] where weaker LR bounds exist [8,23]. However, many questions remain open.…”