Many-body delocalization dynamics in long Aubry-André quasiperiodic chains

Abstract

We study quench dynamics in an interacting spin chain with a quasi-periodic on-site field, known as the interacting Aubry-André model of many-body localization. Using the time-dependent variational principle, we assess the late-time behavior for chains up to L = 50. We find that the choice of periodicity Φ of the quasi-periodic field influences the dynamics. For Φ = ( √ 5 − 1)/2 (the inverse golden ratio) and interaction ∆ = 1, the model most frequently considered in the literature, we obtain the critical disorder Wc = 4.8 ± 0.5 in units where the non-interacting transition is at W = 2. At the same time, for periodicity Φ = √ 2/2 we obtain a considerably higher critical value, Wc = 7.8 ± 0.5. Finite-size effects on the critical disorder Wc are much weaker than in the purely random case. This supports the enhancement of Wc in the case of a purely random potential by rare "ergodic spots," which do not occur in the quasi-periodic case. Further, the data suggest that the decay of the antiferromagnetic order in the delocalized phase is faster than a power law. arXiv:1901.06971v5 [cond-mat.dis-nn]

Finite-Size scaling analysis of many-body localization transition in quasi-periodic spin chains

“…This is also motivated by similar studies on quenched disordered systems that found a linear drift in critical disorder strength with increasing length [20,37,60]. While few previous studies have commented on this behavior being relatively weak for QP systems (thus emphasizing that QP systems are relatively stable) [69,77,81], to the best of our knowledge these have not been based on substantial quantitative arguments.…”

“…The distribution P (ε) has characteristic peaks at = ±2π sin(πk). The value of ε determines how resonant the local tunneling is, strongly affecting system properties both for non-interacting models [94] as well as for the MBL transition [69]. It seems reasonable to us that the characteristic shape of P (ε) for the QP potential determines the double peak structure of P(s z ).…”

“…The phenomenon of MBL may also occur when the random disorder (RD) in the system is replaced by a quasiperiodic (QP) potential [63][64][65][66][67][68][69][70][71]. MBL in QP systems was studied in a number of experimental settings [72][73][74][75] (we note that the RD could, in principle, be introduced in such systems via a speckle potential [76]).…”

Characterizing the many-body localization transition by the dynamics of diagonal entropy

“…Recent developments of quantum simulation based on ultracold atoms [5][6][7][8][9], trapped ions [10], and superconduction circuits [11][12][13][14] with small coupling to thermal environment pave the way for studying MBL in large-scale systems beyond classical exact diagonalization calculations. Several characteristic dynamical properties of MBL, such as the logarithmic spreading of entanglement entropy (EE) [11,[15][16][17][18][19][20] and quantum Fisher information [10,21,22], and the power-law decay of imbalance [5][6][7][8][23][24][25][26], are observed.…”

Diffusive transport in a quasiperiodic Fibonacci chain: Absence of many-body localization at weak interactions

“…In the absence of rare regions (like in quasiperiodic systems), however, one therefore expects only diffusive transport all the way to the MBL transition. Indeed for the interacting AAH model [40][41][42][43][44][45][46][47][48][49][50][51][52][53] , this was to a certain extend observed 48,50 , see however e.g. Refs.…”