Probing entanglement in a many-body–localized system

Lukin, Alexander; Rispoli, Matthew; Schittko, Robert; Tai, M. Eric; Kaufman, Adam M.; Choi, Soonwon; Khemani, Vedika; Léonard, Julian; Greiner, Markus

doi:10.1126/science.aau0818

Cited by 551 publications

(472 citation statements)

References 55 publications

(53 reference statements)

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“…Indeed, if the decomposition (2.9) into each sector is associated with a symmetry such as the projection Π k is that into a specific charged sector of the symmetry, the entropy (2.10) is nothing but the symmetry resolved entanglement entropy [40,41]. We will see that this is the case for indistinguishable particles, and the decomposition (2.9) will be done based on the particle numbers in the subsystem A as done in [42]. The Rényi entropy is also defined as…”

Section: Jhep08(2021)046mentioning

confidence: 99%

“…Note that ρ 0,A = 1. The decomposition (2.58) is the same as that done in [42] based on the particle number conservation. The classical part S cl is the entropy for the fluctuation of the particle numbers in the subsystem A, and the quantum part S q is the configurational entanglement entropy which is the weighed sum of the entanglement entropy for each particle-number sector [42].…”

Section: )mentioning

confidence: 99%

“…42) with (anti-)symmetrization O( x σ , x σ ) = (±) σσ O( x, x ). The projected operators Π k (A)OΠ k (A), which can be regarded as operators in L(H k ), are computed as…”

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confidence: 99%

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Target space entanglement in quantum mechanics of fermions and matrices

Sugishita

2021

J. High Energ. Phys.

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We consider entanglement of first-quantized identical particles by adopting an algebraic approach. In particular, we investigate fermions whose wave functions are given by the Slater determinants, as for singlet sectors of one-matrix models. We show that the upper bounds of the general Rényi entropies are N log 2 for N particles or an N × N matrix. We compute the target space entanglement entropy and the mutual information in a free one-matrix model. We confirm the area law: the single-interval entropy for the ground state scales as $$ \frac{1}{3} $$ 1 3 log N in the large N model. We obtain an analytical $$ \mathcal{O}\left({N}^0\right) $$ O N 0 expression of the mutual information for two intervals in the large N expansion.

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Section: Jhep08(2021)046mentioning

confidence: 99%

Section: )mentioning

confidence: 99%

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Target space entanglement in quantum mechanics of fermions and matrices

Sugishita

2021

J. High Energ. Phys.

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“…Another exciting contemporary development is the experimental realization of novel phases of matter with no equilibrium counterpart, such as the Many-Body Localized (MBL) phase [11][12][13][14] seen in isolated disordered many-body quantum systems which fail to thermalize. Recent experimental advances in quantum simulators have allowed highly precise control over disordered many-body systems and led to evidence of MBL behavior in a number of platforms, ranging from one and two dimensional arrays of ultracold atoms [15][16][17][18][19] to ion traps with programmable random disorder [20,21] and dipolar systems made by nuclear spins [22,23].…”

Section: Introductionmentioning

confidence: 99%

Flow equations for disordered Floquet systems

2021

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In this work, we present a new approach to disordered, periodically driven (Floquet) quantum many-body systems based on flow equations. Specifically, we introduce a continuous unitary flow of Floquet operators in an extended Hilbert space, whose fixed point is both diagonal and time-independent, allowing us to directly obtain the Floquet modes. We first apply this method to a periodically driven Anderson insulator, for which it is exact, and then extend it to driven many-body localized systems within a truncated flow equation ansatz. In particular we compute the emergent Floquet local integrals of motion that characterise a periodically driven many-body localized phase. We demonstrate that the method remains well-controlled in the weakly-interacting regime, and allows us to access larger system sizes than accessible by numerically exact methods, paving the way for studies of two-dimensional driven many-body systems.

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“…Such a decomposition occurs in a number of different contexts (see for instance [56,[78][79][80][81]), where the first term of (B.1) has been called configurational or accessible entropy, while the second term is known as fluctuation, measurement or number entropy defined as…”

Section: B Probability Factors For the Decomposition Into Twisted Sectorsmentioning

confidence: 99%

Illuminating entanglement shadows of BTZ black holes by a generalized entanglement measure

Gerbershagen

2021

J. High Energ. Phys.

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We define a generalized entanglement measure in the context of the AdS/CFT correspondence. Compared to the ordinary entanglement entropy for a spatial subregion dual to the area of the Ryu-Takayanagi surface, we take into account both entanglement between spatial degrees of freedom as well as between different fields of the boundary theory. Moreover, we resolve the contribution to the entanglement entropy of strings with different winding numbers in the bulk geometry. We then calculate this generalized entanglement measure in a thermal state dual to the BTZ black hole in the setting of the D1/D5 system at and close to the orbifold point. We find that the entanglement entropy defined in this way is dual to the length of a geodesic with non-zero winding number. Such geodesics probe the entire bulk geometry, including the entanglement shadow up to the horizon in the one-sided black hole as well as the wormhole growth in the case of a two-sided black hole for an arbitrarily long time. Therefore, we propose that the entanglement structure of the boundary state is enough to reconstruct asymptotically AdS3 geometries up to extremal surface barriers.

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Probing entanglement in a many-body–localized system

Cited by 551 publications

References 55 publications

Target space entanglement in quantum mechanics of fermions and matrices

Target space entanglement in quantum mechanics of fermions and matrices

Flow equations for disordered Floquet systems

Illuminating entanglement shadows of BTZ black holes by a generalized entanglement measure

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