Signatures of many-body localization in the dynamics of two-site entanglement

Iemini, Fernando; Russomanno, Angelo; Rossini, Davide; Scardicchio, Antonello; Fazio, Rosario

doi:10.1103/physrevb.94.214206

Cited by 64 publications

(64 citation statements)

References 67 publications

(127 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…With so many important and interesting properties shown in this one-dimensional (1D) incommensurate model, the Anderson localization phase transition has been one of the most extensively explored phenomena. Besides, recent studies on the many-body localization phase transition in the AAH model with interactions between the neighboring sites endows such systems with more exciting features [20][21][22][23]. Moreover, many generalized AAH models with exotic characteristics have been proposed, such as the AAH model with p-wave superconducting (SC) pairing terms [14,24,25].…”

Section: Introductionmentioning

confidence: 99%

Quench dynamics in the Aubry–André–Harper model with p-wave superconductivity

2018

View full text Add to dashboard Cite

The Anderson localization phase transition in the Aubry-André-Harper (AAH) model with p-wave superconducting (SC) pairing is numerically investigated by suddenly changing the on-site potential from zero to various finite values which fall into the extended, critical and localized phase regimes shown in this model. The time evolution of entanglement entropy (EE), mean width of wave packets and Loschmidt echo of the system exhibit distinct but consistent dynamical signatures in those three phases. Specifically, the EE grows as a power function of time with the exponent of which varies in the extended phase but keeps almost unchanged in the critical phase for different quench parameters. However, if the system is in the localized phase after a quench, the EE grows much slower and will soon get saturated. The time-dependent width of wave packets in the system shows similar behaviors as the EE. In addition, from the perspective of the dynamical phase transition, we find that the Loschmidt echo oscillates and always keeps finite when the system is quenched in the extended phase. In contrast, in the critical or localized phase, the echo will reach to zero at some time intervals or will decay almost to zero after a long-time evolution. The universal features of these quantities in the critical phase of the system with various SC pairing amplitudes are also observed.

show abstract

Section: Introductionmentioning

confidence: 99%

Quench dynamics in the Aubry–André–Harper model with p-wave superconductivity

2018

View full text Add to dashboard Cite

show abstract

“…A plausible explanation for the increase in η as one approaches the MBLT from the ergodic side is that proximal spins become off-resonant so that bonding (bipartite entanglement) takes place at increasingly longer scales-a process that is not possible if the spins are part of a large multipartite entangled block. We note several interesting approaches that made use of the two-site concurrence [58,59] or mutual information [60], which despite revealing other interesting features, such as scaling, do not show a divergence in the localization length from both sides of the transition. An alternative approach for identifying the diverging length scale on the ergodic side based on the entanglement spectrum has been recently developed in Ref.…”

mentioning

confidence: 99%

Many-body localization transition: Schmidt gap, entanglement length, and scaling

Gray¹,

Bose²,

Bayat³

2018

Phys. Rev. B

View full text Add to dashboard Cite

Many-body localization has become an important phenomenon for illuminating a potential rift between nonequilibrium quantum systems and statistical mechanics. However, the nature of the transition between ergodic and localized phases in models displaying many-body localization is not yet well understood. Assuming that this is a continuous transition, analytic results show that the length scale should diverge with a critical exponent ν 2 in one-dimensional systems. Interestingly, this is in stark contrast with all exact numerical studies which find ν ∼ 1. We introduce the Schmidt gap, new in this context, which scales near the transition with an exponent ν > 2 compatible with the analytical bound. We attribute this to an insensitivity to certain finite-size fluctuations, which remain significant in other quantities at the sizes accessible to exact numerical methods. Additionally, we find that a physical manifestation of the diverging length scale is apparent in the entanglement length computed using the logarithmic negativity between disjoint blocks.

show abstract

“…Our results provide important insight into the nature of the ergodic-MBL transition and highlight the care that must be taken in choosing suitable figures of merit to assess such systems. Such an observation is particularly important in the context of the recent experimental [22] and theoretical [30] developments in studying MBL systems where the initial state is fixed.…”

Section: Discussionmentioning

confidence: 99%

Dynamics and asymptotics of correlations in a many-body localized system

2017

View full text Add to dashboard Cite

Abstract.We examine the dynamics of nearest-neighbor bipartite concurrence and total correlations in the spin-1/2 XXZ model with random fields. We show, starting from factorized random initial states, that the concurrence can suffer entanglement sudden death in the long time limit and therefore may not be a useful indicator of the properties of the system. In contrast, we show that the total correlations capture the dynamics more succinctly, and further reveal a fundamental difference in the dynamics governed by the ergodic versus many-body localized phases, with the latter exhibiting dynamical oscillations. Finally, we consider an initial state composed of several singlet pairs and show that by fixing the correlation properties, while the dynamics do not reveal noticeable differences between the phases, the long-time values of the correlation measures appear to indicate the critical region.

show abstract

Signatures of many-body localization in the dynamics of two-site entanglement

Cited by 64 publications

References 67 publications

Quench dynamics in the Aubry–André–Harper model with p-wave superconductivity

Quench dynamics in the Aubry–André–Harper model with p-wave superconductivity

Many-body localization transition: Schmidt gap, entanglement length, and scaling

Dynamics and asymptotics of correlations in a many-body localized system

Contact Info

Product

Resources

About