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arXiv:2105.06346 · Physical Review A

Delocalization of quantum information in long-range interacting systems

Darvin Wanisch, S. Fritzsche

Published Oct 7, 2021• 9 citations
arXivHTMLPDF

Abstract

We investigate the delocalization of quantum information in the nonequilibrium dynamics of the $XY$ spin chain with asymptotically decaying interactions $\ensuremath{\sim}1/{r}^{\ensuremath{\alpha}}$. As a figure of merit, we employ the tripartite mutual information (TMI), the sign of which indicates if quantum information is predominantly shared globally. Interestingly, the sign of the TMI distinguishes regimes of the exponent $\ensuremath{\alpha}$ that are known for different behaviors of information propagation. While an effective causal region bounds the propagation of information, if interactions decay sufficiently fast, this information is mainly delocalized, which leads to the necessity of global measurements. Furthermore, the results indicate that mutual information is monogamous for all possible partitionings in this case, implying that quantum entanglement is the dominant correlation. If interactions decay sufficiently slow, though information can propagate (quasi-)instantaneously, it is mainly accessible by local measurements at early times. Furthermore, it takes some finite time until correlations start to become monogamous, which suggests that entanglement is not the dominant correlation at early times. Our findings give new insights into the dynamics and structure of quantum information in many-body systems with long-range interactions, and might get verified on state-of-the-art experimental platforms.

DOI
10.1103/physreva.104.042409

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We investigate the delocalization of quantum information in the nonequilibrium dynamics of the XYXYXY spin chain with asymptotically decaying interactions \ensuremath∼1/r\ensuremathα\ensuremath{\sim}1/{r}^{\ensuremath{\alpha}}\ensuremath∼1/r\ensuremathα. As a figure of merit, we employ the tripartite mutual information (TMI), the sign of which indicates if quantum information is predominantly shared globally. Interestingly, the sign of the TMI distinguishes regimes of the exponent \ensuremathα\ensuremath{\alpha}\ensuremathα that are known for different behaviors of information propagation. While an effective causal region bounds the propagation of information, if interactions decay sufficiently fast, this information is mainly delocalized, which leads to the necessity of global measurements. Furthermore, the results indicate that mutual information is monogamous for all possible partitionings in this case, implying that quantum entanglement is the dominant correlation. If interactions decay sufficiently slow, though information can propagate (quasi-)instantaneously, it is mainly accessible by local measurements at early times. Furthermore, it takes some finite time until correlations start to become monogamous, which suggests that entanglement is not the dominant correlation at early times. Our findings give new insights into the dynamics and structure of quantum information in many-body systems with long-range interactions, and might get verified on state-of-the-art experimental platforms.
We systematically investigate scrambling (or delocalizing) processes of quantum information encoded in quantum many-body systems by using numerical exact diagonalization. As a measure of scrambling, we adopt the tripartite mutual information (TMI) that becomes negative when quantum information is delocalized. We clarify that scrambling is an independent property of the integrability of Hamiltonians; TMI can be negative or positive for both integrable and nonintegrable systems. This implies that scrambling is a separate concept from conventional quantum chaos characterized by nonintegrability. Specifically, we argue that there are a few exceptional initial states that do not exhibit scrambling, and show that such exceptional initial states have small effective dimensions. Furthermore, we calculate TMI in the Sachdev-Ye-Kitaev (SYK) model, a fermionic toy model of quantum gravity. We find that disorder does not make scrambling slower but makes it smoother in the SYK model, in contrast to many-body localization in spin chains.
Quantum information spreading and scrambling in many-body systems attract interest these days. Tripartite mutual information (TMI) based on operator-based entanglement entropy (EE) is an efficient tool for measuring them. In this paper, we study random spin chains that exhibit phase transitions accompanying nontrivial changes in topological properties. In their phase diagrams, there are two types of many-body localized (MBL) states and one thermalized regime intervening these two MBL states. Quench dynamics of the EE and TMI display interesting behaviors, providing an essential perspective concerning the encoding of quantum information. In particular, one of the models is self-dual, but information spreading measured by the TMI does not respect this self-duality. We investigate this phenomenon from the viewpoint of spatial structure of the stabilizers. In general, we find that knowledge of the phase diagram corresponding to the qubit system is useful for understanding the nature of quantum information spreading in that system. The connection between the present paper and random circuit of projective measurements and also topological Majorana quantum memory is remarked upon.
The nonequilibrium response of a quantum many-body system defines its fundamental transport properties and how initially localized quantum information spreads. However, for long-range-interacting quantum systems little is known. We address this issue by analyzing a local quantum quench in the long-range Ising model in a transverse field, where interactions decay as a variable power law with distance ∝r(-α), α>0. Using complementary numerical and analytical techniques, we identify three dynamical regimes: short-range-like with an emerging light cone for α>2, weakly long range for 1<α<2 without a clear light cone but with a finite propagation speed of almost all excitations, and fully nonlocal for α<1 with instantaneous transmission of correlations. This last regime breaks generalized Lieb-Robinson bounds and thus locality. Numerical calculation of the entanglement spectrum demonstrates that the usual picture of propagating quasiparticles remains valid, allowing an intuitive interpretation of our findings via divergences of quasiparticle velocities. Our results may be tested in state-of-the-art trapped-ion experiments.
The tripartite information (TMI) has emerged as a tool to sieve quantum correlations in quantum many-body systems. A negative TMI is interpreted as evidence for quantum information delocalization in chaotic systems. Here, the authors show that a negative TMI can appear in out-of-equilibrium free-fermion models, and it is linked to the presence of entangled multiplets of excitations. Negative TMI signals a weakening of the relationship between entanglement and thermodynamics, which can be understood in a generalized quasiparticle picture framework.
Entanglement dynamics depend not only on how a quantum system is partitioned, but critically on how interactions across that partition are structured. For a spatial bipartition of a locally interacting system, entanglement is generated near the boundary and then propagates into the bulk. By contrast, when two extended quantum fields are coupled locally along their entire length, the interaction crosses the field-space partition everywhere, and this generates correlations throughout the system. Here, we study the entanglement dynamics between two gapless one-dimensional quantum many-body systems described by Luttinger liquid theory. The systems are initially decoupled and prepared at zero or finite temperature, after which a time-dependent tunneling interaction is activated uniformly along their length. Within a Gaussian approximation, we derive general analytical expressions for the logarithmic negativity, mutual information, and Rényi entropies under arbitrary coupling protocols. At zero temperature, entanglement displays an early-time power-law growth whose exponent is fixed solely by the first non-null derivative of the tunneling protocol. Once the coupling saturates, we obtain exact long-time averages of the information-theoretic quantities and characterise how the correlations scale with temperature and the final coupling strength. We also analyse how mutual information and logarithmic negativity approach the adiabatic limit for a very slow protocol with respect to intrinsic system timescale. This work extends the study of entanglement dynamics in nonequilibrium field theory to field-space partitions and mixed initial states.
Understanding the dynamics of many-body systems is crucial for understanding, e.g., thermalization or transmission of information. Nevertheless, little is known in the case of quantum systems with long-range interactions. Here, we analyze the long-range Ising model in a transverse field, where interactions decay as a power-law with distance ∝r−α\propto r^{-\alpha}∝r−α, α>0\alpha>0α>0. Using complementary numerical and analytical techniques, we identify three dynamical regimes: short-range-like with an emerging light cone for α>2\alpha>2α>2; weakly long-range for 1<α<21<\alpha<21<α<2 without a clear light cone but with a finite propagation speed of excitations; and fully non-local for α<1\alpha<1α<1 with instantaneous transmission of correlations. This last regime breaks generalized Lieb--Robinson bounds. Numerical calculation of the entanglement spectrum demonstrates that the usual picture of propagating quasi-particles remains valid for long-range interactions. This allows an intuitive interpretation in terms of qualitative changes to the spin-wave dispersion, leading to diverging quasi-particle velocities in the long-range regime. Our results may be tested in state-of-the-art trapped-ion experiments.