2019
DOI: 10.1103/physrevb.100.104204
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Slow dynamics and strong finite-size effects in many-body localization with random and quasiperiodic potentials

Abstract: We investigate charge relaxation in disordered and quasi-periodic quantum-wires of spin-less fermions (t−V -model) at different inhomogeneity strength W in the localized and nearly-localized regime. Our observable is the time-dependent density correlation function, Φ(x, t), at infinite temperature. We find that disordered and quasi-periodic models behave qualitatively similar: Although even at longest observation times the width ∆x(t) of Φ(x, t) does not exceed significantly the noninteracting localization len… Show more

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Cited by 84 publications
(66 citation statements)
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References 72 publications
(99 reference statements)
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“…Its exact evolution using standard Hamiltonian diagonalization approach would be a formidable task. On the contrary, Chebyshev polynomial expansion of the time-evolution operator [40] used already a few times in the context of MBL [45][46][47] allows us to obtain numerically exact time-evolution up to quite long times. Those results serve as benchmarks against which we compare the performance of tDMRG and TDVP.…”
Section: Mps Time Evolution Versus "Exact" Resultsmentioning
confidence: 99%
“…Its exact evolution using standard Hamiltonian diagonalization approach would be a formidable task. On the contrary, Chebyshev polynomial expansion of the time-evolution operator [40] used already a few times in the context of MBL [45][46][47] allows us to obtain numerically exact time-evolution up to quite long times. Those results serve as benchmarks against which we compare the performance of tDMRG and TDVP.…”
Section: Mps Time Evolution Versus "Exact" Resultsmentioning
confidence: 99%
“…Ref. [56] studies similarities and differences between the quasiperiodic case and the purely random case by using exact diagonalization and inspecting the behavior of a running exponent β(t) (distinct from our β(t)) defined from the spatial spreading of the diffusive propagator with time, similarly to a previous work studying the purely random case [57]. The focus of Ref.…”
Section: Discussionmentioning
confidence: 99%
“…While the model (1) has been studied in great detail, the critical disorder is only known with a large margin of error, W c = 3.8 ± 1 [22,[31][32][33][34]. We therefore focus on quite strong disorder strengths to be sufficiently far from the critical regime, which is known to exhibit strong finite size effects [35][36][37].…”
mentioning
confidence: 99%