Entangling power of time-evolution operators in integrable and nonintegrable many-body systems

Pal, Rajarshi; Lakshminarayan, Arul

doi:10.48550/arxiv.1805.11632

Cited by 3 publications

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“…Note added. After this work was completed we learned about the very recent paper [40], in which the time dependence of the entangling power of the unitary operator describing periodically kicked many-body system was used to detect non-integrability of the underlying dynamics.…”

Section: Discussionmentioning

confidence: 99%

Bipartite unitary gates and billiard dynamics in the Weyl chamber

2018

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Long time behavior of a unitary quantum gate U, acting sequentially on two subsystems of dimension N each, is investigated. We derive an expression describing an arbitrary iteration of a two-qubit gate making use of a link to the dynamics of a free particle in a 3D billiard. Due to ergodicity of such a dynamics an average along a trajectory V t stemming from a generic two-qubit gate V in the canonical form tends for a large t to the average over an ensemble of random unitary gates distributed according to the flat measure in the Weyl chamber -the minimal 3D set containing points from all orbits of locally equivalent gates. Furthermore, we show that for a large dimension N the mean entanglement entropy averaged along a generic trajectory coincides with the average over the ensemble of random unitary matrices distributed according to the Haar measure on U(N 2 ).

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Section: Discussionmentioning

confidence: 99%

Bipartite unitary gates and billiard dynamics in the Weyl chamber

2018

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“…where U AB ( ) → 1 as → 0. It is assumed that for = 0 both V AB and U AB ( ) break the dynamical symmetry, (see [50,51] for a discussion of operator entanglement) and hence provide a genuine interaction between the two subystems. If = 0, the eigenstates of H(0) (or U(0)) are product states, which are unentangled by definition.…”

Section: Entanglement In Bipartite Systemsmentioning

confidence: 99%

Eigenstate entanglement between quantum chaotic subsystems: Universal transitions and power laws in the entanglement spectrum

et al. 2018

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We derive universal entanglement entropy and Schmidt eigenvalue behaviors for the eigenstates of two quantum chaotic systems coupled with a weak interaction. The progression from a lack of entanglement in the noninteracting limit to the entanglement expected of fully randomized states in the opposite limit is governed by the single scaling transition parameter, Λ. The behaviors apply equally well to few-and many-body systems, e.g. interacting particles in quantum dots, spin chains, coupled quantum maps, and Floquet systems as long as their subsystems are quantum chaotic, and not localized in some manner. To calculate the generalized moments of the Schmidt eigenvalues in the perturbative regime, a regularized theory is applied, whose leading order behaviors depend on √ Λ. The marginal case of the 1/2 moment, which is related to the distance to closest maximally entangled state, is an exception having a √ Λ ln Λ leading order and a logarithmic dependence on subsystem size. A recursive embedding of the regularized perturbation theory gives a simple exponential behavior for the von Neumann entropy and the Havrda-Charvát-Tsallis entropies for increasing interaction strength, demonstrating a universal transition to nearly maximal entanglement. Moreover, the full probability densities of the Schmidt eigenvalues, i.e. the entanglement spectrum, show a transition from power laws and Lévy distribution in the weakly interacting regime to random matrix results for the strongly interacting regime. The predicted behaviors are tested on a pair of weakly interacting kicked rotors, which follow the universal behaviors extremely well.

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“…Unfortunately, very few explicit results are available for realistic systems, although calculations in conformal field theories (CFTs) with large central charge [4][5][6][7], holographic setups [8], and mean-field-like models [9] provide useful insights. Several tools have been proposed to diagnose scrambling, such as the tripartite information [10][11][12][13], out-of-time-order correlators [3,[14][15][16][17][18], and entanglement of operators [19][20][21][22][23][24][25][26][27][29][30][31][32][33][34][35].…”

Section: Introductionmentioning

confidence: 99%

Quantum information scrambling after a quantum quench

Alba

Calabrese

2019

Phys. Rev. B

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How quantum information is scrambled in the global degrees of freedom of non-equilibrium manybody systems is a key question to understand local thermalization. A consequence of scrambling is that in the scaling limit the mutual information information between two intervals vanishes at all times, i.e., it does not exhibit a peak at intermediate times.Here we investigate the mutual information scrambling after a quantum quench in both integrable and non-integrable one dimensional systems. We study the mutual information between two intervals of finite length as a function of their distance. In integrable systems, the mutual information exhibits an algebraic decay with the distance between the intervals, signalling weak scrambling. This behavior may be qualitatively understood within the quasiparticle picture for the entanglement spreading. In the scaling limit of large intervals, times, and distances between the intervals, with their ratios fixed, this predicts a decay exponent equal to 1/2. Away from the scaling limit, the power-law behavior persists, but with a larger (and model-dependent) exponent. For non-integrable models, a much faster decay is observed, which can be attributed to the finite life time of the quasiparticles: unsurprisingly, non-integrable models are better scramblers. arXiv:1903.09176v2 [cond-mat.stat-mech]

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Entangling power of time-evolution operators in integrable and nonintegrable many-body systems

Cited by 3 publications

References 0 publications

Bipartite unitary gates and billiard dynamics in the Weyl chamber

Bipartite unitary gates and billiard dynamics in the Weyl chamber

Eigenstate entanglement between quantum chaotic subsystems: Universal transitions and power laws in the entanglement spectrum

Quantum information scrambling after a quantum quench

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