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Register a new userQuantization of Out-of-Time-Ordered Correlators in non-Hermitian Chaotic Systems
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Wen-Lei Zhao
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This letter reports the findings of the late time behavior of the out-of-time-ordered correlators (OTOCs) via a quantum kicked rotor model with $cal{PT}$-symmetric driving potential. An analytical expression of the OTOCs quadratic growth with time is yielded as $C(t)=G(K)t^2$. Interestingly, the growth rate $G$ features a quantized response to the increase of the kick strength $K$, which indicates the chaos-assisted quantization in the OTOCs dynamics. The physics behind this is the quantized absorption of energy from the non-Hermitian driving potential. This discovery and the ensuing establishment of the quantization mechanism in the dynamics of quantum chaos with non-Hermiticity will provide insights in chaotic dynamics, promising unprecedented observations in updated experiments.
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The out-of-time-ordered correlator (OTOC) is central to the understanding of information scrambling in quantum many-body systems. In this work, we show that the OTOC in a quantum many-body system close to its critical point obeys dynamical scaling laws which are specified by a few universal critical exponents of the quantum critical point. Such scaling laws of the OTOC imply a universal form for the butterfly velocity of a chaotic system in the quantum critical region and allow one to locate the quantum critical point and extract all universal critical exponents of the quantum phase transitions. We numerically confirm the universality of the butterfly velocity in a chaotic model, namely the transverse axial next-nearest-neighbor Ising model, and show the feasibility of extracting the critical properties of quantum phase transitions from OTOC using the Lipkin-Meshkov-Glick (LMG) model.
The out-of-time-order correlator (OTOC), recently analyzed in several physical contexts, is studied for low-dimensional chaotic systems through semiclassical expansions and numerical simulations. The semiclassical expansion for the OTOC yields a leading-order contribution in $hbar^2$ that is exponentially increasing with time within an intermediate, temperature-dependent, time-window. The growth-rate in such a regime is governed by the Lyapunov exponent of the underlying classical system and scales with the square-root of the temperature.
Out-of-time-ordered correlators (OTOCs) have been proposed as a tool to witness quantum information scrambling in many-body system dynamics. These correlators can be understood as averages over nonclassical multi-time quasi-probability distributions (QPDs). These QPDs have more information, and their nonclassical features witness quantum information scrambling in a more nuanced way. However, their high dimensionality and nonclassicality make QPDs challenging to measure experimentally. We focus on the topical case of a many-qubit system and show how to obtain such a QPD in the laboratory using circuits with three and four sequential measurements. Averaging distinct values over the same measured distribution reveals either the OTOC or parameters of its QPD. Stronger measurements minimize experimental resources despite increased dynamical disturbance.
Interacting many-body quantum systems show a rich array of physical phenomena and dynamical properties, but are notoriously difficult to study: they are challenging analytically and exponentially difficult to simulate on classical computers. Small-scale quantum information processors hold the promise to efficiently emulate these systems, but characterizing their dynamics is experimentally challenging, requiring probes beyond simple correlation functions and multi-body tomographic methods. Here, we demonstrate the measurement of out-of-time-ordered correlators (OTOCs), one of the most effective tools for studying quantum system evolution and processes like quantum thermalization. We implement a 3x3 two-dimensional hard-core Bose-Hubbard lattice with a superconducting circuit, study its time-reversibility by performing a Loschmidt echo, and measure OTOCs that enable us to observe the propagation of quantum information. A central requirement for our experiments is the ability to coherently reverse time evolution, which we achieve with a digital-analog simulation scheme. In the presence of frequency disorder, we observe that localization can partially be overcome with more particles present, a possible signature of many-body localization in two dimensions.
Chaotic dynamics in quantum many-body systems scrambles local information so that at late times it can no longer be accessed locally. This is reflected quantitatively in the out-of-time-ordered correlator of local operators, which is expected to decay to zero with time. However, for systems of finite size, out-of-time-ordered correlators do not decay exactly to zero and in this paper we show that the residual value can provide useful insights into the chaotic dynamics. When energy is conserved, the late-time saturation value of the out-of-time-ordered correlator of generic traceless local operators scales as an inverse polynomial in the system size. This is in contrast to the inverse exponential scaling expected for chaotic dynamics without energy conservation. We provide both analytical arguments and numerical simulations to support this conclusion.
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