Abstract Quantum link models (QLMs) serve as experimentally accessible platforms for studying lattice gauge theories with finite-dimensional Hilbert spaces. In this work, we investigate information scrambling in the partially confined phase of a spin-1 quantum link model by calculating the dynamics of out-of-time-ordered correlators (OTOCs) and entanglement entropy. We observe that, in the partially confined phase, information scrambling exhibits significant asymmetry, manifested as the unidirectional propagation of both OTOCs and entanglement entropy. This phenomenon stands in stark contrast to the isotropic spreading observed in the deconfined phase and the localization characteristic of the confined phase. Furthermore, the simultaneous occurrence of the unidirectional propagation of both OTOCs and entanglement entropy, together with the θ -induced asymmetric excitation propagation, reveals a direct connection between information scrambling and charge confinement.
Abstract Quantum link models (QLMs) serve as experimentally accessible platforms for studying lattice gauge theories with finite-dimensional Hilbert spaces. In this work, we investigate information scrambling in the partially confined phase of a spin-1 quantum link model by calculating the dynamics of out-of-time-ordered correlators (OTOCs) and entanglement entropy. We observe that, in the partially confined phase, information scrambling exhibits significant asymmetry, manifested as the unidirectional propagation of both OTOCs and entanglement entropy. This phenomenon stands in stark contrast to the isotropic spreading observed in the deconfined phase and the localization characteristic of the confined phase. Furthermore, the simultaneous occurrence of the unidirectional propagation of both OTOCs and entanglement entropy, together with the θ -induced asymmetric excitation propagation, reveals a direct connection between information scrambling and charge confinement.
A closed quantum system never forgets its initial state, but the encoded information can get scrambled and become inaccessible without measuring a large fraction of all the system degrees of freedom. This scrambling can be diagnosed by studying the spatial spreading of initially local operators under the Heisenberg time evolution, and the decay of the out-of-time-ordered correlators (OTOC). What insights can OTOCs provide to understand the dynamics of quantum many-body systems? What are the characteristic behaviors of OTOCs during the time evolution? How is information scrambling affected by the dissipation in open quantum many-body systems? We first study slow scrambling in many-body localized systems via calculating various correlators, two-point retarded correlators and OTOCs. Comparing with retarded correlators, OTOCs provide more information about the dynamics. We find that disorder slows and partially halts the onset of information scrambling. Instead of ballistic spreading, propagation of information forms a logarithmic light cone. Next, we study the finite-size scaling of OTOCs at late times in generic thermalizing quantum many-body systems. When energy is conserved, the late-time saturation value of the OTOC 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 also study information scrambling in open quantum many-body systems. We define a dissipative version of OTOC and study its behaviors in a prototypical chaotic quantum chain with dissipation. We find that dissipation leads to not only the overall decay of the scrambled information due to leaking, but also structural changes so that the information light cone can only reach a finite distance even when the effect of overall decay is removed. Finally, we construct a family of local Hamiltonians for understanding the asymmetric information scrambling. Our models live on a one-dimensional lattice and exhibit asymmetric butterfly light cone between the left and right spatial directions.
How fast quantum information scrambles such that it becomes inaccessible by local probes turns out to be central to various fields. Motivated by recent works on spin systems with nonlocal interactions, we study information scrambling in different variants of the Ising model. Our work reveals that nonlocal interactions can induce operator dynamics not precisely captured by out-of-time-order correlators (OTOCs). In particular, the operator size exhibits a slowdown in systems with generic power-law interactions despite a highly nonlinear light cone. A recently proposed microscopic model for fast scrambling does not show this slowdown, which uncovers a distinct analogy between a local operator under unitary evolution and the entanglement entropy following a quantum quench. Our work gives new insights on scrambling properties of systems in reach of current quantum simulation platforms and complements results on possibly observing features of quantum gravity in the laboratory.
Abstract The field of information scrambling has seen significant growth over the last decade, where the out-of-time-ordered correlator (OTOC) has emerged as a prominent tool to probe it. In this work, we use bipartite OTOC, a particular form of OTOC, to study information scrambling in the atom–field interaction models and the model of the Ising spin chain interacting with a tilted magnetic field. This is done considering the effects of open quantum systems. A relationship between information scrambling, using bipartite OTOC, and irreversibility, using entropy production, is probed under unitary dynamics. The equivalence of bipartite OTOC with operator entanglement is explicitly shown for the Ising model.
We study the dynamics of out-of-time-ordered correlators (OTOCs) and the entanglement of entropy as quantitative measures of information propagation in disordered many-body systems exhibiting Floquet time-crystal (FTC) phases. We find that an OTOC spreads in the FTC with different characteristic timescales due to the existence of a preferred ``quasiprotected'' direction, denoted as the $\ensuremath{\ell}$-bit direction, along which the spins stabilize their period-doubling magnetization for exponentially long times. While orthogonal to this direction the OTOC thermalizes as an usual many-body localization time-independent system (at stroboscopic times), along the $\ensuremath{\ell}$-bit direction the system features a more complex structure. The scrambling appears as a combination of an initially frozen dynamics (while in the stable period-doubling magnetization time window) and a later logarithmic slow growth (over its decoherence regime) until full thermalization. Interestingly, in the late-time regime, since the wave front propagation of correlations has already settled through the whole chain, scrambling occurs at the same rate regardless of the distance between the spins, thus resulting in an overall envelopelike structure of all OTOCs, independent of their distance, merging into a single growth. In addition, the entanglement entropy shows a logarithmic growth over all time, reflecting the slow dynamics up to a thermal volume-law saturation.
Local excitations as carriers of quantum information spread out in the system in ways governed by the underlying interaction and symmetry. Understanding this phenomenon, also called quantum scrambling, is a prerequisite for employing interacting systems for quantum information processing. The character and direction dependence of quantum scrambling can be inferred from the out-of-time-ordered commutators (OTOCs) containing information on correlation buildup and entanglement spreading. Employing OTOC, we study and quantify the directionality of quantum information propagation in oxide-based helical spin systems hosting a spin-driven ferroelectric order. In these systems, magnetoelectricity permits the spin dynamics and associated information content to be controlled by an electric field coupled to the emergent ferroelectric order. We show that topologically nontrivial quantum phases, such as chiral or helical spin ordering, allow for electric-field controlled anisotropic scrambling and a direction-dependent buildup of quantum correlations. Based on general symmetry considerations, we find that starting from a pure state (e.g., the ground state) or a finite temperature state is essential for observing directional asymmetry in scrambling. In the systematic numerical studies of OTOC on finite-size helical multiferroic chains, we quantify the directional asymmetry of the scrambling and verify the conjectured form of the OTOC around the ballistic wavefront. The obtained direction-dependent butterfly velocity vB(n) provides information on the speed of the ballistic wavefront. In general, our calculations show an early time power-law behavior of OTOC, as expected from an analytic expansion for small times. The long-time behavior of OTOC reveals the importance of (non)integrability of the underlying Hamiltonian as well as the implications of conserved quantities such as the z projection of the total spin. The results point to the potential of spin-driven ferroelectric materials for the use in solid-state-based quantum information processing.
Quantum computing has introduced new paradigms in how information is stored, processed, and transmitted. Unlike classical computation, where data follows deterministic pathways, quantum systems display complex interactions driven by superposition and entanglement. One of the most powerful tools for studying these interactions is the Out-of-Time-Ordered Correlator (OTOC), a mathematical framework used to quantify how information disperses and becomes scrambled in quantum systems. This paper explores information scrambling dynamics in simulated quantum environments using OTOC-based analysis. Rather than relying on a specific quantum processor, this study uses computational simulations to emulate noisy and noise-mitigated conditions, analyzing how OTOC behavior varies across these regimes. Through numerical modeling and circuit-level quantum simulations, the study demonstrates how information spreads, how chaos develops, and how error mitigation influences the stability of information propagation. The findings provide theoretical foundations for designing stable, error-tolerant quantum algorithms and highlight the intersection between quantum physics, computer science, and information theory.