Quench Dynamics of Rényi Negativities and the Quasiparticle Picture

Murciano, Sara; Alba, Vincenzo; Calabrese, Pasquale

doi:10.1007/978-3-031-03998-0_14

Cited by 4 publications

(4 citation statements)

References 128 publications

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“…The logarithmic negativity has been employed to characterize entanglement in systems of harmonic oscillators [19,[53][54][55][56][57][58], spin models [22,[59][60][61][62][63][64][65][66][67][68][69][70], Conformal Field Theory (CFT) [18,[71][72][73][74][75][76][77]. The out-of-equilibrium dynamics after quantum quenches has received a lot of attention [23,31,[78][79][80][81][82][83][84]. In particular, it has been shown in Ref.…”

Section: Fermionic Logarithmic Negativity: Definitionsmentioning

confidence: 99%

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Logarithmic negativity in out-of-equilibrium open free-fermion chains: An exactly solvable case

Alba,

Carollo

2023

SciPost Phys.

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We derive the quasiparticle picture for the fermionic logarithmic negativity in a tight-binding chain subject to gain and loss dissipation. We focus on the dynamics after the quantum quench from the fermionic Néel state. We consider the negativity between both adjacent and disjoint intervals embedded in an infinite chain. Our result holds in the standard hydrodynamic limit of large subsystems and long times, with their ratio fixed. Additionally, we consider the weakly-dissipative limit, in which the dissipation rates are inversely proportional to the size of the intervals. We show that the negativity is proportional to the number of entangled pairs of quasiparticles that are shared between the two intervals, as is the case for the mutual information. Crucially, in contrast with the unitary case, the negativity content of quasiparticles is not given by the Rényi entropy with Rényi index 1/21/2, and it is in general not easily related to thermodynamic quantities.

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Section: Fermionic Logarithmic Negativity: Definitionsmentioning

confidence: 99%

“…Clearly, Θ 2 (k) appears in the quasiparticle picture for the mutual information between two intervals (see for instance [83]). This happens because both the mutual information and the negativity are proportional to the number of pairs shared between A 1 and A 2 .…”

Section: Fermionic Logarithmic Negativitymentioning

confidence: 99%

Logarithmic negativity in out-of-equilibrium open free-fermion chains: An exactly solvable case

Alba,

Carollo

2023

SciPost Phys.

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“…Besides the negativity, the moments of the partial transpose, or the PPT − n conditions, can be employed to quantify entanglement in many-body systems. The PPT − n conditions can be also measured experimentally [4], and admit a quasiparticle picture interpretation [59]. Some results are also available for disordered out-of-equilibrium systems [60].…”

Section: Entanglement Negativity For Fermionic Systems: Definitionsmentioning

confidence: 95%

Entanglement negativity in a fermionic chain with dissipative defects: exact results

Caceffo¹,

Alba²

2023

J. Stat. Mech.

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We investigate the dynamics of the fermionic logarithmic negativity in a free-fermion chain with a localized loss, which acts as a dissipative impurity. The chain is initially prepared in a generic Fermi sea. In the standard hydrodynamic limit of large subsystems and long times, with their ratio fixed, the negativity between two subsystems is described by a simple formula, which depends only on the effective absorption coefficient of the impurity. The negativity grows linearly at short times, then saturating to a volume-law scaling. Physically, this reflects the continuous production with time of entangling pairs of excitations at the impurity site. Interestingly, the negativity is not the same as the Rényi mutual information with Rényi index 1 / 2 , in contrast with the case of unitary dynamics. This reflects the interplay between dissipative and unitary processes. The negativity content of the entangling pairs is obtained in terms of an effective two-state mixed density matrix for the subsystems. Criticality in the initial Fermi sea is reflected in the presence of logarithmic corrections. The prefactor of the logarithmic scaling depends on the loss rate, suggesting a nontrivial interplay between dissipation and criticality.

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“…In integrable models, the quasiparticle picture [27-29, 51, 52] describes the growth of entanglement in time after a global quench, in terms of ballistic propagation of pairs of quasiparticles of opposite momentum, that spread entanglement and correlations through the system. In the case of disjoint subsystems, the quasiparticle picture can be adapted to describe the dynamics of the mutual information [41] and the entanglement negativity [53]. The quasiparticle picture also describes the growth of symmetry-resolved entanglement [54][55][56], and it has recently been generalized to the case of dissipative free fermionic and bosonic systems [57][58][59][60][61].…”

Section: For a Tripartite Systemmentioning

confidence: 99%

Analytical results for the entanglement dynamics of disjoint blocks in the XY spin chain

Parez

Bonsignori

2022

J. Phys. A: Math. Theor.

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The study of the dynamics of entanglement measures after a quench has become a very active area of research in the last two decades, motivated by the development of experimental techniques. However, exact results in this context are available in only very few cases. In this work, we present the proof of the quasiparticle picture for the dynamics of entanglement entropies for two disjoint blocks in the XY chain after a quantum quench. As a byproduct, we also prove the quasiparticle conjecture for the mutual information in that model. Our calculations generalize those presented in [M. Fagotti, P. Calabrese, Phys. Rev. A 78, 010306 (2008)] to the case where the correlation matrix is a block-Toeplitz matrix, and rely on the multidimensional stationary phase approximation in the scaling limit. We also test the quasiparticle predictions against exact numerical calculations, and ﬁnd excellent agreement. In the case of three blocks, we show that the tripartite information vanishes when at least two blocks are adjacent.

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Quench Dynamics of Rényi Negativities and the Quasiparticle Picture

Cited by 4 publications

References 128 publications

Logarithmic negativity in out-of-equilibrium open free-fermion chains: An exactly solvable case

Logarithmic negativity in out-of-equilibrium open free-fermion chains: An exactly solvable case

Entanglement negativity in a fermionic chain with dissipative defects: exact results

Analytical results for the entanglement dynamics of disjoint blocks in the XY spin chain

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