Closure of the entanglement gap at quantum criticality: The case of the quantum spherical model

Wald, Sascha; Arias, Raúl; Alba, Vincenzo

doi:10.1103/physrevresearch.2.043404

Cited by 9 publications

(14 citation statements)

References 107 publications

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“…An intriguing question is how local dissipation affects the entanglement scaling at finite-temperature critical points. An ideal setup to explore this is provided by the so-called quantum spherical model, for which entanglement properties can be studied effectively [78][79][80] . Furthermore, it would be of interest to study how localized gain/loss dissipations may affect entanglement spreading, for instance, by studying the dynamics of the logarithmic negativity [81][82][83][84] and comparing with the quasiparticle picture 85 .…”

Section: Discussionmentioning

confidence: 99%

Noninteracting fermionic systems with localized losses: Exact results in the hydrodynamic limit

Alba,

Carollo

2021

Preprint

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We investigate the interplay between unitary dynamics after a quantum quench and localized dissipation in a noninteracting fermionic chain. In particular, we consider the effect of gain and loss processes, for which fermions are added and removed incoherently. We focus on the hydrodynamic limit of large distances from the source of dissipation and of long times, with their ratio being fixed. In this limit, the localized dissipation gives rise to an effective delta potential (dissipative impurity), and the time-evolution of the local correlation functions admits a simple hydrodynamic description in terms of the fermionic occupations in the initial state and the reflection and transmission amplitudes of the impurity. We derive this hydrodynamic framework from the ab initio calculation of the microscopic dynamics. This allows us to analytically characterize the effect of dissipation for several theoretically relevant initial states, such as a uniform Fermi sea, homogeneous product states, or the inhomogeneous state obtained by joining two Fermi seas. In this latter setting, when both gain and loss processes are present, we observe the emergence of exotic nonequilibrium steady states with stepwise uniform density profiles. In all instances, for strong dissipation the coherent dynamics of the system is arrested, which is a manifestation of the celebrated quantum Zeno effect.

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Section: Discussionmentioning

confidence: 99%

Noninteracting fermionic systems with localized losses: Exact results in the hydrodynamic limit

Alba,

Carollo

2021

Preprint

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“…In particular, the behavior of the entanglement gap has been addressed in proximity of QCPs of various models (see, e.g., Refs. [460,461,[482][483][484][485][486]).…”

Section: S(lmentioning

confidence: 99%

Coherent and dissipative dynamics at quantum phase transitions

Rossini

Vicari

2021

Physics Reports

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“…The scaling of the entanglement gap in the ordered phase of the 2D quantum spherical model was derived analytically in Ref. [36] (see also [63]). Interestingly, it was argued that in general the closure of the entanglement gap is not associated with criticality [19,64].…”

Section: Introductionmentioning

confidence: 99%

“…Quite generically, critical behavior in quantum and classical spherical models is in the universality class of the O(N ) vector model [71] with N → ∞ [72,66,67]. The O(N ) model and the spherical model are also valuable to investigate entanglement properties [73,74,75,76,77,63,36]. Here we consider the one-dimensional QSM with long range couplings.…”

Section: Introductionmentioning

confidence: 99%

Entanglement gap in 1D long-range quantum spherical models

Wald¹,

Arias²,

Alba³

2023

Preprint

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We investigate the finite-size scaling of the entanglement gap in the onedimensional long-range quantum spherical model (QSM). We focus on the weak longrange QSM, for which the thermodynamic limit is well-defined. This model exhibits a continuous phase transition, separating a paramagnetic from a ferromagnet phase. The universality class of the transition depends on the long-range exponent α. We show that in the thermodynamic limit the entanglement gap is finite in the paramagnetic phase, and it vanishes in the ferromagnetic phase. In the ferromagnetic phase the entanglement gap is understood in terms of standard magnetic correlation functions. The entanglement gap decays as δξ ≃ C α L −(1 2−α 4) , where the constant C α depends on the low-energy properties of the model. This reflects that the lower part of the dispersion is affected by the long range physics. Finally, multiplicative logarithmic corrections are absent in the scaling of the entanglement gap, in contrast with the higher-dimensional case.

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Closure of the entanglement gap at quantum criticality: The case of the quantum spherical model

Cited by 9 publications

References 107 publications

Noninteracting fermionic systems with localized losses: Exact results in the hydrodynamic limit

Noninteracting fermionic systems with localized losses: Exact results in the hydrodynamic limit

Coherent and dissipative dynamics at quantum phase transitions

Entanglement gap in 1D long-range quantum spherical models

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