Exact mobility edges for 1D quasiperiodic models

Wang, Yongjian; Xu, Xin; You, Jiangong; Zhang, Zheng; Zhou, Qi

doi:10.48550/arxiv.2110.00962

Cited by 6 publications

(9 citation statements)

References 60 publications

(109 reference statements)

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“…This transition occurring in the behaviour of conductance as a function of µ at every band edge is exactly similar to localization-delocalization transitions as a function of energy, occurring in certain one dimensional quasiperiodic systems, i.e, in systems where the period of the on-site potential is incommensurate with that of the lattice (for example, [33][34][35][36][37][38]). The energy where such a transition occurs in presence of disordered or quasiperiodic potentials is called the mobility edge.…”

supporting

confidence: 57%

Universal subdiffusive behavior at band edges from transfer matrix exceptional points

Saha¹,

Agarwalla²,

Kulkarni³

et al. 2022

Preprint

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Understanding symmetries and transitions in non-Hermitian matrices and their physical consequences is of tremendous interest in the context of open quantum systems. The spectrum of one dimensional tight-binding chain with periodic on-site potential can be obtained by casting the problem in terms of 2 × 2 transfer matrices. We find that these non-Hermitian matrices have a symmetry akin to parity-time symmetry, and hence show transitions across exceptional points. The exceptional points of the transfer matrix of a unit cell correspond to the band edges of the spectrum. When connected to two zero temperature baths at two ends, this consequently leads to subdiffusive scaling of conductance with system size, with an exponent 2, if the chemical potential of the baths are equal to the band edges. We further demonstrate the existence of a dissipative quantum phase transition as the chemical potential is tuned across any band edge. Remarkably, this feature is analogous to transition across a mobility edge in quasi-periodic systems. This behavior is universal, irrespective of the details of the periodic potential and the number of bands of the underlying lattice. It, however, has no analog in absence of the baths.

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supporting

confidence: 57%

Universal subdiffusive behavior at band edges from transfer matrix exceptional points

Saha¹,

Agarwalla²,

Kulkarni³

et al. 2022

Preprint

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“…Moreover, while certain arguments we present depend on some specific aspects of the Maryland model, the crucial part of the proof: sharp analysis of the effect of anti-resonances, is actually quite robust, and we expect it to be useful in the study of other one-frequency quasiperiodic models with unbounded potentials that have attracted attention recently [38,39,40,51] . Additionally, in the models that lead to singular Jacobi matrices (that is where the off-diagonal terms can approach zero) positions of off-diagonal exponential near-zeros also compensate for resonant small divisors, thus creating effective anti-resonances.…”

Section: Introductionmentioning

confidence: 85%

Anti-resonances and sharp analysis of Maryland localization for all parameters

Han¹,

Jitomirskaya²,

Yang³

2022

Preprint

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“…( 13) reduces to the AAH model for b = 0, the model with b = 0 exhibits an exact mobility edge following the expression E = 2 sgn(λ)(1 − |λ|)/b. The LE for the localized state can be obtained from κ(E) = max {κ c (E), 0} with the analytical expression of κ c (E) given by [66,67]…”

mentioning

confidence: 99%

Exponential size scaling of Liouvillian gap in boundary-dissipated systems with Anderson localization

Zhou,

Wang,

Chen

2022

Preprint

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Liouvillian gap plays an important role in describing the asymptotic dynamics of quantum dissipative system. While the Liouvillian gap displays a power-law size scaling in boundary-dissipated systems with diffusive transport, its size-scaling relation is still not known in the presence of Anderson localization. In this letter, we study the Liouvillian gap of various one-dimensional quasiperiodic and disorder systems with boundary dissipation and unveil that Liouvillian gap fulfills an exponential scaling relation ∆g ∝ e −aL in the localized phase. By scrutinizing the extended Aubry-André-Harper model, we fit the value of a and find it coinciding pretty well with the analytical result of Lyapunov exponent κ which is the inverse of localization length ξ. We further apply the perturbation theory to derive ∆g ∝ e −L/ξ analytically. The exponential scaling relation was verified to hold true in other one-dimensional quasiperiodic and random disorder models. We also examine the relaxation time and show the inverse of Liouvillian gap giving a reasonable time scale for the system achieving the steady state.

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Exact mobility edges for 1D quasiperiodic models

Cited by 6 publications

References 60 publications

Universal subdiffusive behavior at band edges from transfer matrix exceptional points

Universal subdiffusive behavior at band edges from transfer matrix exceptional points

Anti-resonances and sharp analysis of Maryland localization for all parameters

Exponential size scaling of Liouvillian gap in boundary-dissipated systems with Anderson localization

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