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arXiv:2305.10245 · Physical review. B./Physical review. B

Negative tripartite mutual information after quantum quenches in integrable systems

Fabio Caceffo, Vincenzo Alba

Published Oct 25, 2023• 14 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.108.134434

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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.
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.
In a non-equilibrium many-body system, the quantum information dynamics between non-complementary regions is a crucial feature to understand the local relaxation towards statistical ensembles. Unfortunately, its characterization is a formidable task, as non-complementary parts are generally in a mixed state. We show that for integrable systems, this quantum information dynamics can be quantitatively understood within the quasiparticle picture for the entanglement spreading. Precisely, we provide an exact prediction for the time evolution of the logarithmic negativity after a quench. In the space-time scaling limit of long times and large subsystems, the negativity becomes proportional to the Rényi mutual information with Rényi index α = 1 / 2 . We provide robust numerical evidence for the validity of our results for free-fermion and free-boson models, but our framework applies to any interacting integrable system.
Tripartite mutual information (TMI) is an efficient observable to quantify the ability of a scrambler for the unitary time-evolution operator with a quenched many-body Hamiltonian. In this paper we give numerical demonstrations of the TMI in disorder-free (translationally invariant) spin models with three-body and four-body multiple-spin interactions. The dynamical behavior of the TMI of these models does not exhibit a linear light cone for sufficiently strong interactions. In early-time evolution, the TMI displays a distinct negative increase fitted by a logarithmiclike function. This is in contrast to the conventional linear light-cone behavior present in the XXZXXZXXZ model and its near-integrable vicinity. The late-time evolution of the TMI in finite-size systems is also numerically investigated. The multiple-spin interactions make the system nearly integrable and weakly suppress the spread of information and scrambling. The observation of the late-time value of the TMI indicates that the scrambling nature of the system changes by interactions and this change can be characterized by a phase-transition-like behavior of the TMI, reflecting the system's integrability and violating the eigenstate thermalization hypothesis.
Quantum information scrambling under the dynamics of a closed many-body system is of wide interest. The tripartite mutual information (TMI) can quantify the scrambling via its stable negative value under temporal evolution. Here, we study the quench dynamics of the TMI in a nonintegrable Ising model with different initial states in the regimes of strong and weak thermalization. Our numerical results show that the most efficient scrambling can occur when the inverse temperatures of initial states are near zero and in the regime of strong thermalization, and weak thermalization accompanies slow scrambling. We then present an experimental protocol for observing strong and weak thermalization in a one-dimensional array of superconducting qubits, based on which the relation between scrambling and the degree of thermalization revealed in this work can be directly verified by superconducting quantum simulators. The inevitable decoherence effects in real situations are also analyzed, paving the way for faithful quantum simulations on actual experimental platforms.
We investigate the delocalization of quantum information in the nonequilibrium dynamics of the XYXYXY 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.
Many-body states that are invariant under particle relabeling, the permutation symmetric states, occur naturally when the system dynamics is described by symmetric processes or collective spin operators. We derive expressions for the reduced density matrix for arbitrary subsystem decomposition for these states and study properties of permutation symmetric states and their subsystems when the joint system is picked randomly and uniformly. Thus defining an appropriate random matrix ensemble, we find the average linear entropy and von Neumann entropy, which implies that random permutation symmetric states are marginally entangled and as a consequence the tripartite mutual information (TMI) is typically positive, preventing information from being shared globally. Applying these results to the quantum kicked top viewed as a multiqubit system, we find that entanglement, mutual information, and TMI all increase for large subsystems across the Ehrenfest or logarithmic time and saturate at the random state values if there is global chaos. During this time the out-of-time-order correlators evolve exponentially, implying scrambling in phase space. We discuss how positive TMI may coexist with such scrambling.