Counting local integrals of motion in disordered spinless-fermion and Hubbard chains

Mierzejewski, Marcin; Kozarzewski, Maciej; Prelovšek, P.

doi:10.1103/physrevb.97.064204

Cited by 58 publications

(51 citation statements)

References 64 publications

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“…This implies that only partial (charge) MBL may occur in the SU(2) symmetric Hubbard chains. This scenario is consistent with the number of local integrals of motion [57] which stays well below the value expected for systems with full MBL. Moreover, one cannot exclude that coupling of localized charges and delocalized spins will eventually delocalize also the charge degrees of freedom [58], even if the latter delocalization will happen at exceedingly long time-scales.…”

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confidence: 82%

Instability of subdiffusive spin dynamics in strongly disordered Hubbard chain

2019

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We study spin transport in a Hubbard chain with strong, random, on-site potential and with spin-dependent hopping integrals, tσ. For the the SU(2) symmetric case, t ↑ = t ↓ , such model exhibits only partial many-body localization with localized charge and (delocalized) subdiffusive spin excitations. Here, we demonstrate that breaking the SU(2) symmetry by even weak spinasymmetry, t ↑ = t ↓ , localizes spins and restores full many-body localization. To this end we derive an effective spin model, where the spin subdiffusion is shown to be destroyed by arbitrarily weak t ↑ = t ↓ . Instability of the spin subdiffusion originates from an interplay between random effective fields and singularly distributed random exchange interactions.

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confidence: 82%

Instability of subdiffusive spin dynamics in strongly disordered Hubbard chain

2019

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“…It has also been found that MBL prevents a driven system from heating [9,[36][37][38][39][40][41]. These unusual properties can be explained via the existence of a macroscopic number of local integrals of motion [12,25,26,[42][43][44][45][46][47].While most of theoretical studies so far concentrated on the one-dimensional (1D) disordered model of interacting spinless fermions, the experiments on MBL are performed on cold-fermion lattices [14,[48][49][50] where the relevant model is the Hubbard model with spin-1/2 fermions, whereby the disorder enters only via a random (or quasi-periodic) charge potential. Recent numerical studies of such a model [47,[51][52][53] reveal that even at strong disorder, localization and nonergodicity occurs only in the charge subsystem, implying a partial MBL.…”

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confidence: 99%

Spin Subdiffusion in the Disordered Hubbard Chain

2018

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We derive and study an effective spin model that explains the anomalous spin dynamics in the one-dimensional Hubbard model with strong potential disorder. Assuming that charges are localized, we show that spins are delocalized and their subdiffusive transport originates from a singular random distribution of spin exchange interactions. The exponent relevant for the subdiffusion is determined by the Anderson localization length and the density of the electrons. Although the analytical derivations are valid for low particle density, numerical results for the full model reveal a qualitative agreement up to half filling.

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“…Many-body localization (MBL) [1,2] is a robust phenomenon of ergodicity breaking in disordered interacting quantum many-body systems [3][4][5][6]. It has attracted considerable attention over the last decade, notable findings include an emergent integrability of MBL phase due to the existence of local integrals of motion (LIOMs) [3,[7][8][9][10] and an associated unbounded logarithmic growth of the bipartite entanglement entropy after a quench from a separable state [11,12]. A wide regime of subdiffusive transport on the ergodic side of the transition was found [13][14][15].…”

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confidence: 99%

Model of level statistics for disordered interacting quantum many-body systems

Sierant

Zakrzewski

2020

Phys. Rev. B

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We numerically study level statistics of disordered interacting quantum many-body systems. A two-parameter plasma model which controls level repulsion exponent β and range h of interactions between eigenvalues is shown to reproduce accurately features of level statistics across the transition from ergodic to many-body localized phase. Analysis of higher order spacing ratios indicates that the considered β-h model accounts even for long range spectral correlations and allows to obtain a clear picture of the flow of level statistics across the transition. Comparing spectral form factors of β-h model and of a system in the ergodic-MBL crossover, we show that the range of effective interactions between eigenvalues h is related to the Thouless time which marks the onset of quantum chaotic behavior of the system. Analysis of level statistics of random quantum circuit which hosts chaotic and localized phases supports the claim that β-h model grasps universal features of level statistics in transition between ergodic and many-body localized phases also for systems breaking time-reversal invariance.Many-body localization (MBL) [1, 2] is a robust phenomenon of ergodicity breaking in disordered interacting quantum many-body systems [3][4][5][6]. It has attracted considerable attention over the last decade, notable findings include an emergent integrability of MBL phase due to the existence of local integrals of motion (LIOMs) [3, 7-10] and an associated unbounded logarithmic growth of the bipartite entanglement entropy after a quench from a separable state [11,12]. A wide regime of subdiffusive transport on the ergodic side of the transition was found [13][14][15]. Signatures of MBL have been observed experimentally in 1D [16,17] and in 2D system [18], however, the stability of MBL in 2D is still debated [19].Spectral statistics of ergodic systems with (without) time reversal invariance follow predictions of Gaussian orthogonal (unitary) ensemble (GOE, GUE, respectively) of random matrices [20,21] while eigenvalues of localized systems are uncorrelated resulting in Poisson statistics (PS). A ratio of consecutive spacings between energy levelswas proposed as a simple probe of the level statistics in [22] with n = 1 and employed in investigation of ergodicity breaking in various settings [23][24][25][26][27][28][29][30]. Higher order spacing ratios (n > 1), studied in [31][32][33][34], are valuable tools to assess properties of level statistics. In contrast to standard measures such as level spacing distribution or number variance they do not require the so called unfolding, i.e. the procedure of setting density of energy levels ρ(E) to unity which can lead to misleading results [35].Recently, an analytical understanding of an appearance of random matrix theory statistics in systems without a clear semiclassical limit have been developed in a periodically driven Ising models [36,37] or in random Floquet circuits [38]. Variants of such systems have been argued to undergo ergodic-MBL transition [39,40].In this work we consider ...

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Counting local integrals of motion in disordered spinless-fermion and Hubbard chains

Cited by 58 publications

References 64 publications

Instability of subdiffusive spin dynamics in strongly disordered Hubbard chain

Instability of subdiffusive spin dynamics in strongly disordered Hubbard chain

Spin Subdiffusion in the Disordered Hubbard Chain

Model of level statistics for disordered interacting quantum many-body systems

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