Quantum chaotic interacting N -particle systems are assumed to show fast and irreversible spreading of quantum information on short (Ehrenfest) time scales ∼ log N . Here we show that, near criticality, certain many-body systems exhibit fast initial scrambling, followed subsequently by oscillatory behavior between reentrant localization and delocalization of information in Hilbert space. We consider both integrable and nonintegrable quantum critical bosonic systems with attractive contact interaction that exhibit locally unstable dynamics in the corresponding many-body phase space of the large-N limit. Semiclassical quantization of the latter accounts for many-body correlations in excellent agreement with simulations. Most notably, it predicts an asymptotically constant local level spacing /τ , again given by τ ∼ log N . This unique timescale governs the long-time behavior of out-of-time-order correlators that feature quasi-periodic recurrences indicating reversibility.The dynamics of quantum information in complex many-body (MB) systems presently attracts a lot of attention [1, 2] ranging from atomic and condensed quantum matter to high energy physics. The evolution of an (excited) quantum MB system towards a state of thermal equilibrium usually goes along with the scrambling of quantum correlations, encoded in the initial state, across the system's many degrees of freedom. Such dynamics requires an improved understanding of MB quantum chaos and the link with thermalization [3-6] and its suppression [1,7,8].Echo protocols, measuring how a perturbation affects successive forward and backward propagations in time, sensitively probe the stability of complex quantum dynamics. Here, out-of-time-order correlators (OTOCs) [9-11]play a central role, with first experimental implementations [12-14], allowing to distinguish various classes of MB systems by their operator growth. On the one side there are slow scramblers, such as systems in the MB localized phase exhibiting logarithmically slow operator spreading [15-18] or, e.g., Luttinger liquids [19] showing only quadratic increase. On the other side, an exponentially fast initial growth of OTOCs is commonly viewed as a quantum signature of MB chaos. Examples comprise systems with holographic duals to black holes [10,20], the SYK-model [11,[21][22][23], and condensed matter systems close to a quantum phase transition (QPT) [24][25][26][27] or exhibiting chaos in the classical limit of large particle number N . In such large-N systems, the exponential growth rate for OTOCs is given by the Lyapunov exponent of their classical counterpart [10,[27][28][29][30][31][32][33][34] and prevails up to the Ehrenfest log N time where MB quantum interference sets in [32,35]. Subsequent OTOC time evolution towards an ergodic limit is then often governed by slow classical modes [36].Here we show that exponentially fast scrambling need not necessarily lead to quantum information loss: There exist systems exhibiting initial growth of complexity without relaxation, i.e., after a quench to ...

We identify a (pseudo) relativistic spin-dependent analogue of the celebrated quantum phase transition driven by the formation of a bright soliton in attractive one-dimensional bosonic gases. In this new scenario, due to the simultaneous existence of the linear dispersion and the bosonic nature of the system, special care must be taken with the choice of energy region where the transition takes place. Still, due to a crucial adiabatic separation of scales, and identified through extensive numerical diagonalization, a suitable effective model describing the transition is found. The corresponding mean-field analysis based on this effective model provides accurate predictions for the location of the quantum phase transition when compared against extensive numerical simulations. Furthermore, we numerically investigate the dynamical exponents characterizing the approach from its finite-size precursors to the sharp quantum phase transition in the thermodynamic limit.

We consider the fate of 1=N expansions in unstable many-body quantum systems, as realized by a quench across criticality, and show the emergence of e 2λt =N as a renormalized parameter ruling the quantum-classical transition and accounting nonperturbatively for the local divergence rate λ of mean-field solutions. In terms of e 2λt =N, quasiclassical expansions of paradigmatic examples of criticality, like the self-trapping transition in an integrable Bose-Hubbard dimer and the generic instability of attractive bosonic systems toward soliton formation, are pushed to arbitrarily high orders. The agreement with numerical simulations supports the general nature of our results in the appropriately combined long-time λt → ∞ quasiclassical N → ∞ regime, out of reach of expansions in the bare parameter 1=N. For scrambling in many-body hyperbolic systems, our results provide formal grounds to a conjectured multiexponential form of out-of-time-ordered correlators.

We present a semiclassical study of the spectrum of a few-body system consisting of two short-range interacting bosonic particles in one dimension, a particular case of a general class of integrable many-body systems where the energy spectrum is given by the solution of algebraic transcendental equations. By an exact mapping between δ-potentials and boundary conditions on the few-body wave functions, we are able to extend previous semiclassical results for single-particle systems with mixed boundary conditions to the two-body problem. The semiclassical approach allows us to derive explicit analytical results for the smooth part of the two-body density of states that are in excellent agreement with numerical calculations. It further enables us to include the effect of bound states in the attractive case. Remarkably, for the particular case of two particles in one dimension, the discrete energy levels obtained through a requantization condition of the smooth density of states are essentially in perfect agreement with the exact ones.

We present analytical results for the nonlocal pair correlations in one-dimensional bosonic systems with repulsive contact interactions that are uniformly valid from the classical regime of high temperatures down to weak quantum degeneracy entering the regime of ultralow temperatures. By using the information contained in the short-time approximations of the full many-body propagator, we derive results that are nonperturbative in the interaction parameter while covering a wide range of temperatures and densities. For the case of three particles we give a simple formula for arbitrary couplings that is exact in the dilute limit while remaining valid up to the regime where the thermal de Broglie wavelength λ T is of the order of the characteristic length L of the system. We then show how to use this result to find analytical expressions for the nonlocal correlations for arbitrary but fixed particle numbers N including finite-size corrections. Neglecting the latter in the thermodynamic limit provides an expansion in the quantum degeneracy parameter Nλ T /L. We compare our analytical results with numerical Bethe ansatz calculations, finding excellent agreement.