Information scrambling at finite temperature in local quantum systems

Abstract

This paper investigates the temperature dependence of quantum information scrambling in local systems with an energy gap, m, above the ground state. We study the speed and shape of growing Heisenberg operators as quantified by out-of-time-order correlators, with particular attention paid to so-called contour dependence, i.e. dependence on the way operators are distributed around the thermal circle. We report large scale tensor network numerics on a gapped chaotic spin chain down to temperatures comparable to the gap which show that the speed of operator growth is strongly contour dependent. The numerics also show a characteristic broadening of the operator wavefront at finite temperature T . To study the behavior at temperatures much below the gap, we perform a perturbative calculation in the paramagnetic phase of a 2+1D O(N ) non-linear sigma model, which is analytically tractable at large N . Using the ladder diagram technique, we find that operators spread at a speed T /m at low temperatures, T m. In contrast to the numerical findings of spin chain, the large N computation is insensitive to the contour dependence and does not show broadening of operator front. We discuss these results in the context of a recently proposed state-dependent bound on scrambling.

The Generalized OTOC from Supersymmetric Quantum Mechanics—Study of Random Fluctuations from Eigenstate Representation of Correlation Functions

“…It is considered to be one of the strongest theoretical probes for quantifying quantum chaos in terms of quantum Lyapunov exponent [9], as well as 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 behavior and information scrambling [14][15][16][17][18][19][20] in the context of many-body quantum systems [21][22][23]. The detailed study of OTOCs reveals an intimate relationship between three entirely different physical concepts, namely holographic duality, quantum chaos, and information scrambling.…”

Scrambling in Yang-Mills

“…The bound limits the growth of commutators [O i (0), O j (t)] where O i ∈ F i so that we are bounding the growth of operators [52]. The growth of operators is a reliable probe of scrambling [27,[53][54][55]. To obtain our bounds, we use arguments of [56], used to derive Lieb-Robinson bounds for general harmonic systems on general lattices.…”

Many-body chaos and anomalous diffusion across thermal phase transitions in two dimensions

“…In quantum systems, truly chaotic behaviour, namely the exponential growth of OTOC [34], can only be observed certain large-N models, e.g. Sachdev-Ye-Kitaev (SYK) and related models dual to black holes [1,3,4,7,10,11,39], other large-N theories [40][41][42], and weakly interacting systems with semiclassical quasiparticle dynamics [43,44]. In these models the exponential growth can be observed over a parametrically long time window between t ∼ λ −1 L and λ −1 L ln N or λ −1 L ln(1/ħ h) for large N or the semiclassical (ħ h → 0) limits, respectively.…”