Spin Subdiffusion in the Disordered Hubbard Chain

We establish rigorously that transport is slower than diffusive for a class of disordered one-dimensional Hamiltonian chains. This is done by deriving quantitative bounds on the variance in equilibrium of the energy or particle current, as a function of time. The slow transport stems from the presence of rare insulating regions (Griffiths regions). In manybody disordered quantum chains, they correspond to regions of anomalously high disorder, where the system is in a localized phase. In contrast, we deal with quantum and classical disordered chains where the interactions, usually referred to as anharmonic couplings in classical systems, are sparse. The system hosts thus rare regions with no interactions and, since the chain is Anderson localized in the absence of interactions, the non-interacting rare regions are insulating. Part of the mathematical interest of our model is that it is one of the few non-integrable models where the diffusion constant can be rigorously proven not to be infinite.

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“…We see hence that, for ℓ = ℓ(t) given by (28), I 2 (t) = O((log t) 4 t ab 2 ). Adding the contributions of I 1 , I 2 , we conclude that…”

Section: Griffiths Regionsmentioning

confidence: 75%

Subdiffusion in One-Dimensional Hamiltonian Chains with Sparse Interactions

2020

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“…It is known that such systems in general exhibit slow dynamics, most notably reflected in subdiffusive trans-port [45,[50][51][52][53][54][55][56][57][60][61][62][63][64], and it was found that slow dynamics is also visible in the spreading of quantum information [65,86], even in the absence of conserved quantities which could be transported [66].…”

Section: Discussionmentioning

confidence: 99%

“…In the vicinity of the MBL transition, the situation is more complicated: At intermediate disorder, where the system still thermalizes, an anomalously slow thermalization [14,[45][46][47][48][49] is found, which was connected to slow, subdiffusive transport [50][51][52][53][54][55][56][57][58][59][60][61][62][63][64]. The anomalous thermalization is also reflected in a sublinear powerlaw growth ∝ t α of the wave function entanglement entropy [65], even in systems which do not have globally conserved densities [66], suggesting that the generic slow dynamics is a universal precursor of MBL.…”

Section: Introductionmentioning

confidence: 99%

Power-law entanglement growth from typical product states

Lezama

Luitz

2019

Phys. Rev. Research

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Generic quantum many-body systems typically show a linear growth of the entanglement entropy after a quench from a product state. While entanglement is a property of the wave function, it is generated by the unitary time evolution operator and is therefore reflected in its increasing complexity as quantified by the operator entanglement entropy.Using numerical simulations of a static and a periodically driven quantum spin chain, we show that there is a robust correspondence between the entanglement entropy growth of typical product states with the operator entanglement entropy of the unitary evolution operator, while special product states, e.g. σz basis states, can exhibit faster entanglement production.In the presence of a disordered magnetic field in our spin chains, we show that both the wave function and operator entanglement entropies exhibit a power-law growth with the same disorderdependent exponent, and clarify the apparent discrepancy in previous results. These systems, in the absence of conserved densities, provide further evidence for slow information spreading on the ergodic side of the many-body localization transition. arXiv:1908.07010v1 [cond-mat.dis-nn]

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“…Moreover, the existence of MBL has been found in a few experimental studies [23-28]. Among several characteristic features of strongly disordered systems is unusually slow time evolution of characteristic physical properties [27,[29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48]] that typically emerges as subdiffusive dynamics as a precursor to MBL transition [18,39,[49][50][51][52][53][54].In this Letter we consider the effect of driving (via the constant electric field) on a quantum particle in a random chain coupled to itinerant hard-core bosons (HCB). We note that such a system simulates the propagation of a (single) charge coupled to spin degrees in strongly correlated systems, as e.g., the disordered Hubbard typemodels [44,55,56], being realized in cold-atom experiments [23][24][25][26][27][28].…”

mentioning

confidence: 99%

“…Moreover, the existence of MBL has been found in a few experimental studies [23][24][25][26][27][28]. Among several characteristic features of strongly disordered systems is unusually slow time evolution of characteristic physical properties [27,[29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48] that typically emerges as subdiffusive dynamics as a precursor to MBL transition [18,39,[49][50][51][52][53][54].…”

mentioning

confidence: 99%

Einstein Relation for a Driven Disordered Quantum Chain in the Subdiffusive Regime

2019

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A quantum particle propagates subdiffusively on a strongly disordered chain when it is coupled to itinerant hard-core bosons. We establish a generalized Einstein relation (GER) that relates such subdiffusive spread to an unusual time-dependent drift velocity, which appears as a consequence of a constant electric field. We show that GER remains valid much beyond the regime of the linear response. Qualitatively, it holds true up to strongest drivings when the nonlinear field-effects lead to the Stark-like localization. Numerical calculations based on full quantum evolution are substantiated by much simpler rate equations for the boson-assisted transitions between localized Anderson states.Introduction-Over two decades after the outstanding discovery of the Anderson localization (AL) phenomena [1], the effect of the interplay between the disorder and many-body interactions on transport properties of metals started to be recognized as one of the fundamental unsolved problems in solid state physics [2,3]. The importance of interactions on AL systems is now identified as a concept of the many-body localization (MBL) [4,5]. The presence of MBL has been theoretically confirmed predominantly in systems that posses only spin or charge degrees of freedom [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]. Moreover, the existence of MBL has been found in a few experimental studies [23-28]. Among several characteristic features of strongly disordered systems is unusually slow time evolution of characteristic physical properties [27,[29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48]] that typically emerges as subdiffusive dynamics as a precursor to MBL transition [18,39,[49][50][51][52][53][54].In this Letter we consider the effect of driving (via the constant electric field) on a quantum particle in a random chain coupled to itinerant hard-core bosons (HCB). We note that such a system simulates the propagation of a (single) charge coupled to spin degrees in strongly correlated systems, as e.g., the disordered Hubbard typemodels [44,55,56], being realized in cold-atom experiments [23][24][25][26][27][28]. It has long been assumed that the AL phenomenon is destroyed by the electron-phonon coupling via the mechanism of phonon-assisted hopping [57,58]. Recently the absence of localization and the onset of normal diffusion of a particle coupled to standard itinerant bosons has been confirmed via a direct quantum evolution [59]. Still, the itinerant HCB appear to be a separate case with a transient or even persistent subdiffusive dynamics [54,60]. While the subdiffusive dynamics has been found in various disordered interacting systems, the behavior of such system under constant driving remains predominantly unexplored [61] whereby in driven MBL systems the focus has been mostly on periodic drivings [9,[62][63][64][65].Transport properties of disordered quantum interacting many-body systems depend on the disorder strength. Weakly disordered systems typically display generic

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Spin Subdiffusion in the Disordered Hubbard Chain

Cited by 57 publications

References 73 publications

Subdiffusion in One-Dimensional Hamiltonian Chains with Sparse Interactions

Subdiffusion in One-Dimensional Hamiltonian Chains with Sparse Interactions

Power-law entanglement growth from typical product states

Einstein Relation for a Driven Disordered Quantum Chain in the Subdiffusive Regime

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