Logarithmic, noise-induced dynamics in the Anderson insulator

Lezama, Talía L. M.; Lev, Yevgeny Bar

doi:10.21468/scipostphys.12.5.174

Cited by 14 publications

(14 citation statements)

References 58 publications

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“…We would like to remark that a rigorous analytical derivation supporting the logarithmic growth of the density profile in the outer regime remains an open and challenging problem. In relation to this we note a recent interesting work in [39] in a much simpler setup involving a single local dephasing connected to an Anderson insulator. This work reported an interesting logarithmic spread in time of density excitation.…”

Section: Localized Phase λ/J>1mentioning

confidence: 73%

“…For example, it was recently shown that for a one-dimensional disordered lattice, displaying Anderson localization, when subjected to a local dephasing, density excitation spreads logarithmically in time [39]. Very recently, this study involving dephasing probes was extended for the incommensurate Aubrey-Andre-Harper (AAH) lattice model [40].…”

Section: J Stat Mech (2024) 063101mentioning

confidence: 99%

“…The impact of dephasing probes on the quantum dynamics of a lattice that is filled with particles has been an active area of research [28-33, 37, 38]. It is also important to note that often such dephasing probe scenario is studied by adding a stochastic noise coupled to a number-conserving term in the Hamiltonian of the lattice [31][32][33][39][40][41][42][43][44].…”

Section: Introductionmentioning

confidence: 99%

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Impact of dephasing probes on incommensurate lattices

Ghosh,

Mohanta,

Kulkarni

et al. 2024

J. Stat. Mech.

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We investigate open quantum dynamics for a one-dimensional incommensurate Aubry–André–Harper lattice chain, a part of which is initially filled with electrons and is further connected to dephasing probes at the filled lattice sites. This setup is akin to a step-initial configuration where the non-zero part of the step is subjected to dephasing. We investigate the quantum dynamics of local electron density, the scaling of the density front as a function of time both inside and outside of the initial step, and the growth of the total number of electrons outside the step. We analyze these quantities in all three regimes, namely, the de-localized, critical, and localized phases of the underlying lattice. Outside the initial step, we observe that the density front spreads according to the underlying nature of single-particle states of the lattice, for both the de-localized and critical phases. For the localized phase, the spread of the density front hints at a logarithmic behavior in time that has no parallel in the isolated case (i.e. in the absence of probes). Inside the initial step, due to the presence of the probes, the density front spreads in a diffusive manner for all the phases. This combination of rich and different dynamical behavior, outside and inside the initial step, results in the emergence of mixed dynamical phases. While the total occupation of electrons remains conserved, the value outside or inside the initial step turns out to have a rich dynamical behavior. Our work is widely adaptable and has interesting consequences when disordered/quasi-disordered systems are subjected to a thermodynamically large number of probes.

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Section: Localized Phase λ/J>1mentioning

confidence: 73%

Section: J Stat Mech (2024) 063101mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Impact of dephasing probes on incommensurate lattices

Ghosh,

Mohanta,

Kulkarni

et al. 2024

J. Stat. Mech.

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“…A localized system is typically a closed system with no transport. Coupling a localized system to a Markovian heat bath induces slow transport for local coupling 55 , 56 or diffusive transport for global coupling 57 – 61 . A similar effect is expected to occur if a Markovian bath is replaced by a sufficiently large thermalizing system.…”

Section: Discussionmentioning

confidence: 99%

Absence of localization in interacting spin chains with a discrete symmetry

et al. 2023

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Novel paradigms of strong ergodicity breaking have recently attracted significant attention in condensed matter physics. Understanding the exact conditions required for their emergence or breakdown not only sheds more light on thermalization and its absence in closed quantum many-body systems, but it also has potential benefits for applications in quantum information technology. A case of particular interest is many-body localization whose conditions are not yet fully settled. Here, we prove that spin chains symmetric under a combination of mirror and spin-flip symmetries and with a non-degenerate spectrum show finite spin transport at zero total magnetization and infinite temperature. We demonstrate this numerically using two prominent examples: the Stark many-body localization system (Stark-MBL) and the symmetrized many-body localization system (symmetrized–MBL). We provide evidence of delocalization at all energy densities and show that delocalization persists when the symmetry is broken. We use our results to construct two localized systems which, when coupled, delocalize each other. Our work demonstrates the dramatic effect symmetries can have on disordered systems, proves that the existence of exact resonances is not a sufficient condition for delocalization, and opens the door to generalization to higher spatial dimensions and different conservation laws.

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“…Khemani et al [28] showed nonlocal response to local manipulations in localized systems. Lezama and Bar Lev [29] studied the dynamics of an AL system with local noise. These works consider time-dependent Hamiltonians, and are thus different from ours.…”

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confidence: 99%

Adding boundary terms to Anderson localized Hamiltonians leads to unbounded growth of entanglement

Huang

2023

EPL

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It is well known that in Anderson localized systems, starting from a random product state the entanglement entropy remains bounded at all times. However, we show that adding a single boundary term to an Anderson localized Hamiltonian leads to unbounded growth of entanglement. Our results imply that Anderson localization is not a local property. One cannot conclude that a subsystem has Anderson localized behavior without looking at the whole system, as a term that is arbitrarily far from the subsystem can aﬀect the dynamics of the subsystem in such a way that the features of Anderson localization are lost.

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Logarithmic, noise-induced dynamics in the Anderson insulator

Cited by 14 publications

References 58 publications

Impact of dephasing probes on incommensurate lattices

Impact of dephasing probes on incommensurate lattices

Absence of localization in interacting spin chains with a discrete symmetry

Adding boundary terms to Anderson localized Hamiltonians leads to unbounded growth of entanglement

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