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arXiv:2408.12533

Tripartite entanglement dynamics following a quantum quench

Clément Berthière

Published Aug 22, 2024• 0 citations
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Abstract

We investigate the dynamics of multipartite entanglement after quenches from initial states which generate multiplets of quasiparticle excitations beyond the usual pair structure. We focus on the dynamics of tripartite entanglement through the lens of the Markov gap -- a computable quantity that signals irreducible tripartite entanglement when positive. In the XX spin chain, we show that the Markov gap is positive at intermediate times, implying the presence of tripartite entanglement. After a time delay, the Markov gap increases and then decays at longer times, thus exhibiting an entanglement barrier. We argue that those qualitative features are consistent with an interpretation of the spreading of tripartite entanglement by triplets of tripartite-entangled quasiparticles.

DOI
10.48550/arxiv.2408.12533

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•Nov 13, 2018•52 citations
We investigate the dynamics of multipartite entanglement after quenches from initial states which generate multiplets of quasiparticle excitations beyond the usual pair structure. We focus on the dynamics of tripartite entanglement through the lens of the Markov gap -- a computable quantity that signals irreducible tripartite entanglement when positive. In the XX spin chain, we show that the Markov gap is positive at intermediate times, implying the presence of tripartite entanglement. After a time delay, the Markov gap increases and then decays at longer times, thus exhibiting an entanglement barrier. We argue that those qualitative features are consistent with an interpretation of the spreading of tripartite entanglement by triplets of tripartite-entangled quasiparticles.
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The quasi-particle picture is a powerful tool to understand the entanglement spreading in many-body quantum systems after a quench. As an input, the structure of the excitations' pattern of the initial state must be provided, the common choice being pairwise-created excitations. However, several cases exile this simple assumption. In this work we investigate weakly-interacting to free quenches in one dimension. This results in a far richer excitations' pattern where multiplets with a larger number of particles are excited. We generalize the quasi-particle ansatz to such a wide class of initial states, providing a small-coupling expansion of the Rényi entropies. Our results are in perfect agreement with iTEBD numerical simulations.
A bstract We study how multipartite entanglement is dynamically reorganized during holographic thermalization following a global quench in AdS 3 /CFT 2 . We first use the n -partite information (− 1) n I n to probe collective multipartite entanglement in holographic configurations where the full n -region entanglement wedge is connected while all fewer-party ones are disconnected, thereby excluding fewer-party contributions. The spatial range of multipartite entanglement first expands and then contracts as the system approaches its late-time locally thermal state. Entanglement involving different numbers of parties develops on comparable early-time scales, while the entanglement that involves more parties relaxes more slowly, revealing a transient propagation from shorter to longer spatial distances. We further compute the Markov gap and the genuine tripartite multi-entropy as complementary probes of tripartite entanglement. The Markov gap can remain enhanced after local thermalization, whereas the genuine tripartite multi-entropy undergoes a nonmonotonic evolution and returns to its vacuum value for the adjacent tripartition considered in this work. These results show that a global quench redistributes the entanglement across spatial scales and reorganizes its multipartite structure.
Abstract A typical working condition in the study of quantum quenches is that the initial state produces a distribution of quasiparticle excitations with an opposite-momentum-pair structure. In this work we investigate the dynamical and stationary properties of the entanglement entropy after a quench from initial states which do not have such structure: instead of pairs of excitations they generate ν -plets of correlated excitations with . Our study is carried out focusing on a system of non-interacting fermions on the lattice. We study the time evolution of the entanglement entropy showing that the standard semiclassical formula is not applicable. We propose a suitable generalisation which correctly describes the entanglement entropy evolution and perfectly matches numerical data. We finally consider the relation between the thermodynamic entropy of the stationary state and the diagonal entropy, showing that when there is no pair structure their ratio depends on the details of the initial state and lies generically between 1/2 and 1.
We investigate entanglement dynamics in bipartite systems governed by inhomogeneous Hamiltonians of the form H=HL+HRH = H_L + H_RH=HL​+HR​, where HL/RH_{L/R}HL/R​ acts only on the left or right region and is homogeneous within each region. Focusing on the XX chain and the transverse-field Ising chain, we derive analytical formulas for the entanglement entropy between the two regions in the hydrodynamic limit of long times. In this regime, fermions incident on the interface undergo scattering, generating entanglement between reflected and transmitted modes. The resulting quasiparticle picture is controlled by the transmission coefficient, which we obtain analytically by solving the stationary lattice Schrödinger equation. Due to the bounded dispersion, strong inhomogeneity suppresses both transport and entanglement growth. We benchmark our analytical predictions against numerical simulations in paradigmatic setups. Finally, we extend the analysis to the interacting XXZ chain using tDMRG. The numerical data show qualitative agreement with the quadratic case: entanglement growth remains suppressed in the strongly inhomogeneous limit. Notably, however, entanglement continues to increase even when transport is suppressed, at least at intermediate times.
A typical working condition in the study of quantum quenches is that the initial state produces a distribution of quasiparticle excitations with an opposite-momentum-pair structure.In this work we investigate the dynamical and stationary properties of the entanglement entropy after a quench from initial states which do not have such structure: instead of pairs of excitations they generate ν-plets of correlated excitations with ν > 2. Our study is carried out focusing on a system of non-interacting fermions on the lattice.We study the time evolution of the entanglement entropy showing that the standard semiclassical formula is not applicable.We propose a suitable generalisation which correctly describes the entanglement entropy evolution and perfectly matches numerical data.We finally consider the relation between the thermodynamic entropy of the stationary state and the diagonal entropy, showing that when there is no pair structure their ratio depends on the details of the initial state and lies generically between 1/2 and 1.