Entanglement tsunami in (<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math>)-dimensions

Leichenauer, Stefan; Moosa, Mudassir

doi:10.1103/physrevd.92.126004

Cited by 51 publications

(82 citation statements)

References 24 publications

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“…According to this conjecture, the calculation of the entanglement in higher dimensions reduces to a deterministic elastic problem for the minimal membrane in space-time. In 1D, it results in particularly simple universal scaling functions, which agree with scaling forms in holographic 1 þ 1D CFTs [8,10,44], and which we suggest are universal for generic, nonintegrable, translationally invariant 1D systems.…”

Section: Introductionsupporting

confidence: 54%

“…For relativistic systems in which the quasiparticle picture holds (rational CFTs), all quasiparticles travel at the same speed, and as a result Eq. (24) does apply [1,3] (however, the entanglement of more complex regions will differ between the quasiparticle picture, on the one hand, and the results from holographic systems and the minimal cut picture, on the other hand [3,4,44]). …”

Section: A Scaling Form For Entanglement Saturationmentioning

confidence: 99%

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Quantum Entanglement Growth under Random Unitary Dynamics

et al. 2017

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Characterizing how entanglement grows with time in a many-body system, for example, after a quantum quench, is a key problem in nonequilibrium quantum physics. We study this problem for the case of random unitary dynamics, representing either Hamiltonian evolution with time-dependent noise or evolution by a random quantum circuit. Our results reveal a universal structure behind noisy entanglement growth, and also provide simple new heuristics for the "entanglement tsunami" in Hamiltonian systems without noise. In 1D, we show that noise causes the entanglement entropy across a cut to grow according to the celebrated KardarParisi-Zhang (KPZ) equation. The mean entanglement grows linearly in time, while fluctuations grow like ðtimeÞ 1=3 and are spatially correlated over a distance ∝ ðtimeÞ 2=3 . We derive KPZ universal behavior in three complementary ways, by mapping random entanglement growth to (i) a stochastic model of a growing surface, (ii) a "minimal cut" picture, reminiscent of the Ryu-Takayanagi formula in holography, and (iii) a hydrodynamic problem involving the dynamical spreading of operators. We demonstrate KPZ universality in 1D numerically using simulations of random unitary circuits. Importantly, the leading-order time dependence of the entropy is deterministic even in the presence of noise, allowing us to propose a simple coarse grained minimal cut picture for the entanglement growth of generic Hamiltonians, even without noise, in arbitrary dimensionality. We clarify the meaning of the "velocity" of entanglement growth in the 1D entanglement tsunami. We show that in higher dimensions, noisy entanglement evolution maps to the wellstudied problem of pinning of a membrane or domain wall by disorder.

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Section: Introductionsupporting

confidence: 54%

Section: A Scaling Form For Entanglement Saturationmentioning

confidence: 99%

Quantum Entanglement Growth under Random Unitary Dynamics

et al. 2017

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“…This should perhaps not be too surprising, since expectations about the entanglement wedge are based on the Ryu-Takayanagi formula for the entanglement entropy. However, it is known that a simple free field model on the boundary will not reproduce the correct RT formula for the entanglement entropy of multiple intervals after a quench [33]. So it may simply be that our weakly-coupled model does not preserve the requisite entanglement between subregions upon evolving to bilocals along a single Cauchy slice.…”

Section: Jhep04(2016)119mentioning

confidence: 97%

Precursors, gauge invariance, and quantum error correction in AdS/CFT

Freivogel

Jefferson

Kabir

2016

J. High Energ. Phys.

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A puzzling aspect of the AdS/CFT correspondence is that a single bulk operator can be mapped to multiple different boundary operators, or precursors. By improving upon a recent model of Mintun, Polchinski, and Rosenhaus, we demonstrate explicitly how this ambiguity arises in a simple model of the field theory. In particular, we show how gauge invariance in the boundary theory manifests as a freedom in the smearing function used in the bulk-boundary mapping, and explicitly show how this freedom can be used to localize the precursor in different spatial regions. We also show how the ambiguity can be understood in terms of quantum error correction, by appealing to the entanglement present in the CFT. The concordance of these two approaches suggests that gauge invariance and entanglement in the boundary field theory are intimately connected to the reconstruction of local operators in the dual spacetime.

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“…A first hint of this was provided by holographic calculations of entanglement entropy [19][20][21], where, even in 1+1 dimensions, entanglement scrambles maximally -late time features in the entanglement entropy of widely separated subsystems, such as the dip in figure 1b, are entirely absent. This apparent discrepancy was first observed in [19] and has also been explored in [22]. Our aim is to reconcile these two pictures, and to understand the middle ground.…”

Section: Jhep09(2015)110mentioning

confidence: 99%

Entanglement scrambling in 2d conformal field theory

Asplund

Bernamonti

Galli

et al. 2015

J. High Energ. Phys.

157

270

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Abstract:We investigate how entanglement spreads in time-dependent states of a 1+1 dimensional conformal field theory (CFT). The results depend qualitatively on the value of the central charge. In rational CFTs, which have central charge below a critical value, entanglement entropy behaves as if correlations were carried by free quasiparticles. This leads to long-term memory effects, such as spikes in the mutual information of widely separated regions at late times. When the central charge is above the critical value, the quasiparticle picture fails. Assuming no extended symmetry algebra, any theory with c > 1 has diminished memory effects compared to the rational models. In holographic CFTs, with c 1, these memory effects are eliminated altogether at strong coupling, but reappear after the scrambling time t β log c at weak coupling.

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Entanglement tsunami in (1+1)-dimensions

Cited by 51 publications

References 24 publications

Quantum Entanglement Growth under Random Unitary Dynamics

Quantum Entanglement Growth under Random Unitary Dynamics

Precursors, gauge invariance, and quantum error correction in AdS/CFT

Entanglement scrambling in 2d conformal field theory

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