Noise, delocalization, and quantum diffusion in one-dimensional tight-binding models

Gholami, Ehsan; Lashkami, Zahra Mohammaddoust

doi:10.1103/physreve.95.022216

Cited by 9 publications

(9 citation statements)

References 67 publications

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“…The effects of localisation could be further investigated, whether taking a more fine-grained look at the unusual Wannier-Stark behaviour in appendix A, or going to much larger system sizes in order to limit the influence of finite size effects. Lastly, quasiperiodic systems such as the Aubry-André model could be considered, where transient effects such as stochastic resonance with anti-localised eigenstates [32] may provide new insights into ENAQT beyond the steady state.…”

Section: Discussionmentioning

confidence: 99%

“…However, in general the long-range interactions in 1D systems prevent full Anderson localisation [28,29], and recent work has shown that homogeneous long-range coupling [30] or coupling to cavities [31] can significantly alter 1D responses to disorder in ways beyond the scope of this paper. Recent years have also seen broad interest in the transient effects of dephasing on quantum diffusion, such as stochastic resonance, and many-body localisation, especially focussed on the quasiperiodic Aubry-André model [12,[32][33][34][35][36][37], as well as quantum chaotic systems Coloured areas show ± one standard deviation, each point is averaged from 100 configurations of disorder. An ordered ( ) and disordered ( ) point are highlighted, and their eigenspectra shown in the centre and right panels, respectively.…”

Section: Figurementioning

confidence: 99%

“…Taking inspiration from a prior study on stochastic resonance [32] we investigated the variance of a time-evolving localised initial state injected onto the centre of a chain of 41 sites. This chain was closed,…”

Section: Data Availability Statementmentioning

confidence: 99%

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Localisation determines the optimal noise rate for quantum transport

Coates

Lovett²,

Gauger³

2021

New J. Phys.

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Environmental noise plays a key role in determining the efficiency of transport in quantum systems. However, disorder and localisation alter the impact of such noise on energy transport. To provide a deeper understanding of this relationship we perform a systematic study of the connection between eigenstate localisation and the optimal dephasing rate in 1D chains. The effects of energy gradients and disorder on chains of various lengths are evaluated and we demonstrate how optimal transport efficiency is determined by both size-independent, as well as size-dependent factors. By discussing how size-dependent influences emerge from finite size effects we establish when these effects are suppressed, and show that a simple power law captures the interplay between size-dependent and size-independent responses. Moving beyond phenomenological pure dephasing, we implement a finite temperature Bloch-Redfield model that captures detailed balance. We show that the relationship between localisation and optimal environmental coupling strength continues to apply at intermediate and high temperature but breaks down in the low temperature limit.

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Section: Discussionmentioning

confidence: 99%

Section: Figurementioning

confidence: 99%

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Localisation determines the optimal noise rate for quantum transport

Coates

Lovett²,

Gauger³

2021

New J. Phys.

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“…[3][4][5] Early studies of the AA model [6][7][8][9][10][11] were focused on the properties of localized eigenfunctions near the transition. Lately, the interest to the AA model has been revived [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26] . Nowadays, it is invoked to study different observable quantities in the presence of the quasiperiodic background.…”

Section: Introductionmentioning

confidence: 99%

Spinful Aubry-André model in a magnetic field: Delocalization facilitated by a weak spin-orbit coupling

Malla

Raǐkh

2018

Phys. Rev. B

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We have incorporated spin-orbit coupling into the Aubry-André model of tight-binding electron motion in the presence of periodic potential with a period incommensurate with lattice constant. This model is known to exhibit an insulator-metal transition upon increasing the hopping amplitude. Without external magnetic field, spin-orbit coupling leads to a simple renormalization of the hopping amplitude. However, when the degeneracy of the on-site energies is lifted by an external magnetic field, the interplay of Zeeman splitting and spin-orbit coupling has a strong effect on the localization length. We studied this interplay numerically by calculating the energy dependence of the Lyapunov exponent in the insulating regime. Numerical results can be unambiguously interpreted in the language of the phase-space trajectories. As a first step, we have explained the plateau in the energy dependence of the localization length in the original Aubry-André model. Our main finding is that a very weak spin-orbit coupling leads to delocalization of states with energies smaller than the Zeeman shift. The origin of the effect is the spin-orbit-induced opening of new transport channels. We have also found that restructuring of the phase-space trajectories, which takes place at certain energies in the insulating regime, causes a singularity in the energy dependence of the localization length. PACS numbers: 73.50.-h, 75.47.-m arXiv:1801.00305v1 [cond-mat.mes-hall]

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“…Different regimes, ranging from a canonical ballistic to subdiffusion (delocalization), has been already studied [26,27] for several kind of randomness and memory. Moreover, non-Markovianity can be explored by means of the historydependence of the paths [28,29] Alternatively, in [30], it was first introduced the possibility of measuring hyperballistic diffusion in 1D (quasi-) lattices, a phenomenon later verified on tight-binding lattice models [31,32], XXZ spin chains [33], phononic heat transport [34] and quantum kicked rotors [35], where α > 2 with α = 3 playing a leading role and the remaining cases with 2 < α < 3 obtained by assuming internal sub-lattices with standard features (for details please consult [36,37]).…”

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confidence: 99%

Elephant quantum walk

2018

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We introduce an analytically treatable discrete time quantum walk in a one-dimensional lattice which combines non-Markovianity and hyperballistic diffusion associated with a Gaussian whose variance, σ 2 t , growing cubicly with time, σ ∝ t 3 . These properties have have been numerically found in several systems, namely tight-binding lattice models. For its rules, our model can be understood as the quantum version of the classical non-Markovian 'elephant random walk' process, for which the quantum coin operator only changes the value of the diffusion constant though, contrarily to the classical coin.a. Introduction. The random walk problem has been a cornerstone in the classical description of systems for which a deterministic approach is either impossible or too complex to be carried out in an efficient way. Equilibrium and non-equilibrium problems like Hamiltonian Monte Carlo, belief propagation, genetic and search algorithms or pricing financial derivatives [1][2][3][4][5] are systematically understood as a random walk in phase-space of the respective system. The first fundamental property of a random walk process, X = {X t }, concerns the time dependence of the variance, σ 2 t ∝ t. Second, because it derives from a Bernoulli process, the random walk, abides by the ubiquitous Markovian property [6], according to which a memoryless random process is defined as a orderly succession of events where the conditional probability distribution of the future state X t (discrete time t > t 0 ) does only depend on its present state, P (X t | X t−1 , . . . , X t0 ) = P (X t | X t−1 ).While in the classical treatment of a Physical system probability is above all a tool for getting quantitative answers, in quantum theory, probability is intrinsic [7] and thus quantum walks emerged as the formal quantum equivalent to random walks [8,9]. Physically, quantum walks describe situations where a quantum particle is moving on a discrete grid, which allows simulating a wide range of transport phenomena [10][11][12][13][14] including the description of some types of topological insulators and yields an important approach in quantum computing processes [15][16][17] . In other words, the particle dynamically explores a large Hilbert space, H P , spanned by its positions on a lattice corresponding to basis states {|l }, (l ∈ Z), that is augmented by a Hilbert space, H C , spanned by the particle internal statese.g. a two-dimensional basis {|↑ , |↓ }. The evolution of a quantum walk on the full Hilbert space, H ≡ H C ⊗ H P , is ruled by the combined application of two unitary operatorsÛwhereÎ is the identity operator on the H P subspace. Bear- * giuseppe.dimolfetta@lis-lab.fr ing in mind the analogy of quantum walks with the classical random walk, the operatorĈ acts on subspace H C and plays the same role as the coin. For that reason, it is named quantum coin and the internal states related to the subspace H C the coin states. On the other hand, the shift operator, S, is state-dependent and following Ref.[8] readŝAssuming the quantum coin...

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Noise, delocalization, and quantum diffusion in one-dimensional tight-binding models

Cited by 9 publications

References 67 publications

Localisation determines the optimal noise rate for quantum transport

Localisation determines the optimal noise rate for quantum transport

Spinful Aubry-André model in a magnetic field: Delocalization facilitated by a weak spin-orbit coupling

Elephant quantum walk

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