Quantum scrambling and state dependence of the butterfly velocity

Abstract

Operator growth in spatially local quantum many-body systems defines a scrambling velocity. We prove that this scrambling velocity bounds the state dependence of the outof-time-ordered correlator in local lattice models. We verify this bound in simulations of the thermal mixed-field Ising spin chain. For scrambling operators, the butterfly velocity shows a crossover from a microscopic high temperature value to a distinct value at temperatures below the energy gap. arXiv:1812.07598v3 [hep-th]

Many-body quantum dynamics slows down at low density

“…More broadly, can we show unambiguously that quantum dynamics has to slow down in any kind of constrained subspace? While this might seem intuitive, and there is certainly evidence for this [13][14][15], proving such a statement has been notoriously challenging, and very few rigorous results are known. The standard approach for constraining quantum dynamics is based on the Lieb-Robinson theorem [16], which applies to operator norms and holds in every state.…”

“…By construction, therefore, Lieb-Robinson bounds are not useful at finding temperaturedependent bounds on quantum dynamics [17]. While recently these techniques have been improved to obtain temperature-dependent bounds on the velocity of information scrambling in one dimensional models [15], the resulting bounds depend on multiple microscopic model details.…”

Quantum information scrambling after a quantum quench

“…Unfortunately, very few explicit results are available for realistic systems, although calculations in conformal field theories (CFTs) with large central charge [4][5][6][7], holographic setups [8], and mean-field-like models [9] provide useful insights. Several tools have been proposed to diagnose scrambling, such as the tripartite information [10][11][12][13], out-of-time-order correlators [3,[14][15][16][17][18], and entanglement of operators [19][20][21][22][23][24][25][26][27][29][30][31][32][33][34][35].…”

THE GENERALIZED OTOC FROM SUPERSYMMETRIC QUANTUM MECHANICS: Study of Random Fluctuations from Eigenstate Representation of Correlation Functions

“…where X 2 and Q 2 can be explicitly evaluated to have the following expressions The symbol γ used in the above equations denotes the following expression γ = p 2 (0) 2 + 8π 4 − p 2 (0) 2 cos(2πx 2 (0)) cosec(πx 2 (0)) (B. 19) The Poisson Bracket of the momentum at different times is symbolically denoted by {p 2 (t 1 ), p 2 (t 2 )} = P 1 /P 2 where P 1 and P 2 represents the following expressions:…”

“…It is considered to be one of the strongest theoretical probe for quantifying quantum chaos in terms of quantum Lyapunov exponent [9], quantum theories of stochasticity and randomness among the theoretical physics community. Besides playing a key role in investigating the holographic duality [10][11][12][13] between a strongly correlated quantum system and a gravitational dual system, it also characterizes the chaotic behaviour and information scrambling [14][15][16][17][18][19] in the context of many-body quantum systems [21][22][23]. The detailed study of OTOCs reveal an intimate relationship between three entirely different physical concepts, namely holographic duality, quantum chaos and information scrambling.…”