Entanglement after quantum quenches in Lifshitz scalar theories

Kim, Keun‐Young; Nishida, Mitsuhiro; Seo, Minsik; Sugimoto, Yuji; Tomiya, Akio

doi:10.1088/1742-5468/ab417f

Cited by 7 publications

(5 citation statements)

References 51 publications

(180 reference statements)

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“…In order to give predictive power to equation (3), one should fix the values of v n (k) and s n (k): the former are the group velocities of the excitations around the stationary state [55,56,100] and the latter are the thermodynamic entropy densities of the GGE [55,56]. The validity of equation (3) has been carefully tested both analytically and numerically in free-fermion and free-boson models [54,[101][102][103][104][105][106][107][108][109][110][111][112][113] and in many interacting integrable models [55,56,[114][115][116][117][118]. The mechanism for the entanglement evolution in chaotic systems is different, not as well understood as in integrable models and with many peculiar features.…”

Section: Scrambling and Entanglement Revivals In Integrable Modelsmentioning

confidence: 99%

Entanglement revivals as a probe of scrambling in finite quantum systems

Modak¹,

Alba²,

Calabrese³

2020

J. Stat. Mech.

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The entanglement evolution after a quantum quench became one of the tools to distinguish integrable versus chaotic (non-integrable) quantum many-body dynamics. Following this line of thoughts, here we propose that the revivals in the entanglement entropy provide a finite-size diagnostic benchmark for the purpose. Indeed, integrable models display periodic revivals manifested in a dip in the block entanglement entropy in a finite system. On the other hand, in chaotic systems, initial correlations get dispersed in the global degrees of freedom (information scrambling) and such a dip is suppressed. We show that while for integrable systems the height of the dip of the entanglement of an interval of fixed length decays as a power law with the total system size, upon breaking integrability a much faster decay is observed, signalling strong scrambling. Our results are checked by exact numerical techniques in free-fermion and free-boson theories, and by time-dependent density matrix renormalisation group in interacting integrable and chaotic models.

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Section: Scrambling and Entanglement Revivals In Integrable Modelsmentioning

confidence: 99%

Entanglement revivals as a probe of scrambling in finite quantum systems

Modak¹,

Alba²,

Calabrese³

2020

J. Stat. Mech.

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“…The Ising model is only one of the many quenches in non-interacting theories of bosons and fermions in which the entanglement evolution is quantitatively captured by Eq. ( 27), as seen numerically in many cases [75,[88][89][90][91][92][93][94][95][96][97][98].…”

Section: The Example Of the Transverse Field Ising Chainmentioning

confidence: 71%

Entanglement spreading in non-equilibrium integrable systems

Calabrese

2020

Preprint

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These are lecture notes for a short course given at the Les Houches Summer School on "Integrability in Atomic and Condensed Matter Physics", in summer 2018.Here, I pedagogically discuss recent advances in the study of the entanglement spreading during the non-equilibrium dynamics of isolated integrable quantum systems. I first introduce the idea that the stationary thermodynamic entropy is the entanglement accumulated during the non-equilibrium dynamics and then use such an idea to provide quantitive predictions for the time evolution of the entanglement entropy in arbitrary integrable models, regardless of the interaction strength.

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“…The validity of Eq. 3 has been tested both analytically and numerically in free-fermion and free-boson models [68,[70][71][72][73][74][75][76][77][78][79][80][81][82] and in many interacting integrable models [69,[83][84][85][86][87].…”

Section: Entanglement Productionmentioning

confidence: 99%

Many-body dynamical phase transition in quasi-periodic potential

Modak,

Rakshit

2021

Preprint

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Much has been learned regarding dynamical quantum phase transition (DQPT) due to sudden quenches across quantum critical points in traditional quantum systems. However, not much has been explored when a system undergoes a localization-delocalization transition. Here, we study one dimensional fermionic systems in presence of a quasi-periodic potential, which induces delocalizationlocalization transition even in 1D. We show signatures of DQPT in the many-body dynamics, when quenching is performed between phases belonging to different universality classes. We investigate how the non-analyticity in the dynamical free energy gets affected with filling fractions in the bare system and, further, study the fate of DQPT under interaction. Strikingly, whenever quenching is performed from the low-entangled localized phase to the high-entangled delocalized phase, our studies suggest an intimate relationship between DQPT and the rate of the entanglement growth -Faster growths of entanglement entropy ensures quicker manifestation of the non-analiticties in the many-body dynamical free energy.

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Entanglement after quantum quenches in Lifshitz scalar theories

Cited by 7 publications

References 51 publications

Entanglement revivals as a probe of scrambling in finite quantum systems

Entanglement revivals as a probe of scrambling in finite quantum systems

Entanglement spreading in non-equilibrium integrable systems

Many-body dynamical phase transition in quasi-periodic potential

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