Transport in the nonergodic extended phase of interacting quasiperiodic systems

Ghosh, Soumi; Gidugu, Jyotsna; Mukerjee, Subroto

doi:10.1103/physrevb.102.224203

Cited by 13 publications

(32 citation statements)

References 46 publications

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“…One is that in the localized phase, − ln IPR q becomes self-averaging, in agreement to what was discussed in Ref. [42]. The other difference is that the values of ν around the critical point become much smaller, but it is still not negative, so the lack of selfaveraging persists.…”

Section: Logarithm Of the Generalized Participation Ratiossupporting

confidence: 84%

“…In contrast, if interactions are added to these systems, the delocalization-localization transition happens already in 1D and for finite disorder strengths, fractality exists even in the MBL phase. For these interacting systems, it is still under debate whether before the MBL phase there is a single critical point or an extended phase where the eigenstates are multifractal [24,[27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42]. In fact, even the very existence of the MBL phase has now gone under debate [43][44][45].…”

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confidence: 99%

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Multifractality and self-averaging at the many-body localization transition

Solórzano,

Santos,

Torres-Herrera

2021

Preprint

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Finite-size effects have been a major and justifiable source of concern for studies of many-body localization, and several works have been dedicated to the subject. In this paper, however, we discuss yet another crucial problem that has received much less attention, that of the lack of selfaveraging and the consequent danger of reducing the number of random realizations as the system size increases. By taking this into account and considering ensembles with a large number of samples for all system sizes analyzed, we find that the generalized dimensions of the eigenstates of the disordered Heisenberg spin-1/2 chain close to the transition point to localization are described remarkably well by an exact analytical expression derived for the non-interacting Fibonacci lattice, thus providing an additional tool for studies of many-body localization.

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Section: Logarithm Of the Generalized Participation Ratiossupporting

confidence: 84%

mentioning

confidence: 99%

Multifractality and self-averaging at the many-body localization transition

Solórzano,

Santos,

Torres-Herrera

2021

Preprint

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“…Whether this phase shrinks in the thermodynamic limit to a critical point or remains of finite width in the parameter space is an open question [60,61]. According to a recent theoretical work, if the non-interacting system has single particle mobility edges, in the corresponding interacting system the nonergodic sub-diffusive phase may persist even in the thermodynamic limit [62]. In our model, we observe a broad non-ergodic sub-diffusive phase for h ≫ 2t 0 , where all the single-particle states are highly localized.…”

Section: Time Evolution Of Density Imbalancementioning

confidence: 99%

Many-body localization and enhanced non-ergodic sub-diffusive regime in the presence of random long-range interactions

Prasad,

Garg

2020

Preprint

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We study many-body localization (MBL) in a one-dimensional system of spinless fermions with a deterministic aperiodic potential in the presence of long-range interactions decaying as power-law Vij/(ri − rj) α with distance and having random coefficients Vij . We demonstrate that MBL survives even for α < 1 and is preceded by a broad non-ergodic sub-diffusive phase. Starting from parameters at which the short-range interacting system shows infinite temperature MBL phase, turning on random power-law interactions results in many-body mobility edges in the spectrum with a larger fraction of ergodic delocalized states for smaller values of α. Hence, the critical disorder h r c , at which ergodic to non-ergodic transition takes place increases with the range of interactions. Time evolution of the density imbalance I(t), which has power-law decay I(t) ∼ t −γ in the intermediate to large time regime, shows that the critical disorder h I c , above which the system becomes diffusionless (with γ ∼ 0) and transits into the MBL phase is much larger than h r c . In between h r c and h I c there is a broad non-ergodic sub-diffusive phase, which is characterized by the Poissonian statistics for the level spacing ratio, multifractal eigenfunctions and a non zero dynamical exponent γ ≪ 1/2. The system continues to be sub-diffusive even on the ergodic side (h < h r c ) of the MBL transition, where the eigenstates near the mobility edges are multifractal. For h < h0 < h r c , the system is super-diffusive with γ > 1/2. The rich phase diagram obtained here is unique to random nature of long-range interactions. We explain this in terms of the enhanced correlations among local energies of the effective Anderson model induced by random power-law interactions.

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“…Introduction: Many-body localization (MBL) is a novel dynamical phenomenon occuring in ioslated manybody quantum systems. It has long been established that the quantum systems may enter MBL phases in the presence of sufficiently strong random disorder [1][2][3][4][5][6][7][8][9][10][11][12] or quasi-periodic (QP) potential [13][14][15][16][17][18] in one-dimensional (1D) systems. In MBL phases, the system fails to thermally equilibrate and exhibits exotic behaviors, such as "area law" entanglement for highly excited states [9][10][11], logarithmic spread of entanglement [8], and emergent local integrals of motion [11,12].…”

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confidence: 99%

Probing many-body localization by excited-state VQE

Liu,

Zhang,

Hsieh

et al. 2021

Preprint

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Non-equilibrium physics including many-body localization (MBL) has attracted increasing attentions, but theoretical approaches of reliably studying non-equilibrium properties remain quite limited. In this Letter, we propose a systematic approach to probe MBL phases on a digital quantum computer via the excited-state variational quantum eigensolver (VQE) and demonstrate convincing results of MBL on a quantum hardware, which we believe paves a promising way for future simulations of non-equilibrium systems beyond the reach of classical computations in the noisy intermediate-scale quantum (NISQ) era. Moreover, the MBL probing protocol based on excitedstate VQE is NISQ-friendly, as it can successfully differentiate the MBL phase from thermal phases with relatively-shallow quantum circuits, and it is also robust against the effect of quantum noises.

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Transport in the nonergodic extended phase of interacting quasiperiodic systems

Cited by 13 publications

References 46 publications

Multifractality and self-averaging at the many-body localization transition

Multifractality and self-averaging at the many-body localization transition

Many-body localization and enhanced non-ergodic sub-diffusive regime in the presence of random long-range interactions

Probing many-body localization by excited-state VQE

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