Boundary chaos

Fritzsch, Felix; Prosen, Tomaž

doi:10.1103/physreve.106.014210

Cited by 5 publications

(12 citation statements)

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“…Namely, spectral fluctuations of the evolution operator coinicide with those of appropriate random matrix ensembles, see App. A, and dynamical correlations decay exponentially in time [65]. In this work we use the simplistic nature of this model to obtain the asymptotics of entanglement dynamics analytically for different classes of impurity interactions, yielding results that seem quite non-intuitive at first glance.…”

Section: Summary Of Resultsmentioning

confidence: 99%

“…This setup was introduced in Ref. [65] and dubbed boundary chaos. One might think of such a circuit as a toy model for a free system subject to a local perturbation which introduces nontrivial scattering to the otherwise free dynamics.…”

Section: Introductionmentioning

confidence: 99%

“…One might think of such a circuit as a toy model for a free system subject to a local perturbation which introduces nontrivial scattering to the otherwise free dynamics. Despite its simple nature the boundary chaos circuit has been shown to be quantum chaotic in the sense of spectral statistics and exhibits ergodic dynamics [65].…”

Section: Introductionmentioning

confidence: 99%

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Boundary chaos: Exact entanglement dynamics

Fritzsch,

Ghosh,

Prosen

2023

SciPost Phys.

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We compute the dynamics of entanglement in the minimal setup producing ergodic and mixing quantum many-body dynamics, which we previously dubbed boundary chaos. This consists of a free, non-interacting brickwork quantum circuit, in which chaos and ergodicity is induced by an impurity interaction, i.e., an entangling two-qudit gate, placed at the system’s boundary. We compute both the conventional bipartite entanglement entropy with respect to a connected subsystem including the impurity interaction for initial product states as well as the so-called operator entanglement entropy of initial local operators. Thereby we provide exact results in a particular scaling limit of both time and system size going to infinity for either very small or very large subsystems. We show that different classes of impurity interactions lead to very distinct entanglement dynamics. For impurity gates preserving a local product state forming the bulk of the initial state, entanglement entropies of states show persistent spikes with period set by the system size and suppressed entanglement in between, contrary to the expected linear growth in ergodic systems. We observe similar dynamics of operator entanglement for generic impurities. In contrast, for T-dual impurities, which remain unitary under partial transposition, we find entanglement entropies of both states and operators to grow linearly in time with the maximum possible speed allowed by the geometry of the system. The intensive nature of interactions in all cases causes entanglement to grow on extensive time scales proportional to system size.

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Section: Summary Of Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Boundary chaos: Exact entanglement dynamics

Fritzsch,

Ghosh,

Prosen

2023

SciPost Phys.

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“…( 40) and the entanglement entropies (41). For various system sizes L we obtain the second Rényi entropy also numerical by contracting the tensor network (65) and depict it in Fig. 4 for subsystem size l + 1 = 3.…”

Section: Generic Impurity Interactionsmentioning

confidence: 99%

“…In Fig. 5(a) we depict the sencond Rényi entropy for various system sizes obtained from contracting the tensor network (65) for l = 0. The asymptotic form of the entropies is approached fast even for moderately large system sizes.…”

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confidence: 99%

Boundary Chaos: Exact Entanglement Dynamics

Fritzsch¹,

Gosh²,

Prosen³

2023

Preprint

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We compute the dynamics of entanglement in the minimal setup producing ergodic and mixing quantum many-body dynamics, which we previously dubbed boundary chaos. This consists of a free, non-interacting brickwork quantum circuit, in which chaos and ergodicity is induced by an impurity interaction, i.e., an entangling two-qudit gate, placed at the system's boundary. We compute both the conventional bipartite entanglement entropy with respect to a connected subsystem including the impurity interaction for initial product states as well as the so-called operator entanglement entropy of initial local operators. Thereby we provide exact results in a particular scaling limit of both time and system size going to infinity for either very small or very large subsystems. We show that different classes of impurity interactions lead to very distinct entanglement dynamics. For impurity gates preserving a local product state forming the bulk of the initial state, entanglement entropies of states show persistent spikes with period set by the system size and suppressed entanglement in between, contrary to the expected linear growth in ergodic systems. We observe similar dynamics of operator entanglement for generic impurities. In contrast, for T-dual impurities, which remain unitary under partial transposition, we find entanglement entropies of both states and operators to grow linearly in time with the maximum possible speed allowed by the geometry of the system. The intensive nature of interactions in all cases cause entanglement to grow on extensive time scales proportional to system size.

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