Rare‐region effects and dynamics near the many‐body localization transition

Agarwal, Kartiek; Altman, Ehud; Demler, Eugene; Gopalakrishnan, Sarang; Huse, David A.; Knap, Michael

doi:10.1002/andp.201600326

Cited by 203 publications

(219 citation statements)

References 119 publications

Supporting

Mentioning

210

Contrasting

Order By: Relevance

“…We have also presented numerical evidence which is inconsistent with the prevailing explanation for subdiffusion in MBL systems, namely the Griffiths picture [7,9,50,51]. The Griffiths picture naturally relies on the presence of uncorrelated quenched disorder in the system, which is crucial for generating a sufficient density of rare blocking inclusions.…”

mentioning

confidence: 71%

See 1 more Smart Citation

Transport in quasiperiodic interacting systems: From superdiffusion to subdiffusion

Lev

Kennes

Klöckner

et al. 2017

EPL

View full text Add to dashboard Cite

Using a combination of numerically exact and renormalization-group techniques we study the nonequilibrium transport of electrons in an one-dimensional interacting system subject to a quasiperiodic potential. For this purpose we calculate the growth of the mean-square displacement as well as the melting of domain walls. While the system is nonintegrable for all studied parameters, there is no finite region of parameters for which we observe diffusive transport. In particular, our model shows a rich dynamical behavior crossing over from superdiffusion to subdiffusion. We discuss the implications of our results for the general problem of many-body localization, with a particular emphasis on the rare region Griffiths picture of subdiffusion.Introduction. -The finite energy transport properties of quantum-mechanical systems generally fall into one of the three standard categories: ballistic, diffusive, and the complete absence of transport altogether. Ballistic transport is only possible in special, so-called integrable cases (such as free fermions) where an extensive set of local conserved quantities prevents currents from scattering. Interacting, clean systems are generically diffusive, while the cessation of transport is a hallmark of systems that completely fail to equilibrate, such as those that undergo Anderson localization [1]. The study of the transition between such regimes has been energized by the recent focus on systems that undergo many-body localization (MBL) [2][3][4]. In the standard quenched disordered variants of such systems, dynamical behavior is observed that exhibits a rich set of distinct transport behaviors [5][6][7][8][9]. Interacting quasiperiodic (QP) systems are also believed to exhibit similar behavior, and are the basis for several recent experimental studies on MBL [10,11]. Unfortunately, very little is known about transport in such systems. Here, we fill this vital gap via a finite-temperature version [12][13][14] of the time-dependent matrix renormalization group (tDMRG) [15,16] as well as the functional renormalization group (FRG) [17,18].Model. -We consider a one-dimensional model of spinless fermions, subject to a quasiperiodic potential (QP),

show abstract

mentioning

confidence: 71%

“…It has been proposed that subdiffusion is a result of rare spatial regions with anomalously large escape times (which for example could correspond to areas with very short local localization lengths) [7,9,50,51]. These rare regions dramatically affect transport in one dimension, since every particle has to pass through all effective barriers.…”

mentioning

confidence: 99%

Transport in quasiperiodic interacting systems: From superdiffusion to subdiffusion

Lev

Kennes

Klöckner

et al. 2017

EPL

View full text Add to dashboard Cite

show abstract

“…[36][37][38], transport is claimed to be subdiffusive and dominated by Griffiths-type dynamics [39,40]. According to the Griffiths phase model of the MBL transition [36,37,41] z is the dynamical exponent associated with the transport which reaches 0.5 z 1 = in the diffusive limit [23]. As the border of MBL phase is approached, the exponent z 1 vanishes.…”

Section: The Imbalance Decaymentioning

confidence: 99%

Many-body localization of bosons in optical lattices

Sierant

Zakrzewski

2018

New J. Phys.

View full text Add to dashboard Cite

Many-body localization for a system of bosons trapped in a one-dimensional lattice is discussed. Two models that may be realized for cold atoms in optical lattices are considered. The model with a random on-site potential is compared with previously introduced random interactions model. While the origin and character of the disorder in both systems is different they show interesting similar properties. In particular, many-body localization appears for a sufficiently large disorder as verified by a time evolution of initial density wave states as well as using statistical properties of energy levels for small system sizes. Starting with different initial states, we observe that the localization properties are energy-dependent which reveals an inverted many-body localization edge in both systems (that finding is also verified by statistical analysis of energy spectrum). Moreover, we consider computationally challenging regime of transition between many body localized and extended phases where we observe a characteristic algebraic decay of density correlations which may be attributed to subdiffusion (and Griffiths-like regions) in the studied systems. Ergodicity breaking in the disordered Bose-Hubbard models is compared with the slowing-down of the time evolution of the clean system at large interactions.

show abstract

“…These rules cleanly prevent unphysical "avalanche" instabilities of the MBL phase [46,52] in which an atypically large resonant cluster becomes increasingly thermal as it grows, enabling it to thermalize an arbitrarily large MBL region [53].…”

mentioning

confidence: 99%

Scaling Theory of Entanglement at the Many-Body Localization Transition

2017

View full text Add to dashboard Cite

We study the universal properties of eigenstate entanglement entropy across the transition between many-body localized (MBL) and thermal phases. We develop an improved real space renormalization group approach that enables numerical simulation of large system sizes and systematic extrapolation to the infinite system size limit. For systems smaller than the correlation length, the average entanglement follows a sub-thermal volume law, whose coefficient is a universal scaling function. The full distribution of entanglement follows a universal scaling form, and exhibits a bimodal structure that produces universal subleading power-law corrections to the leading volume-law. For systems larger than the correlation length, the short interval entanglement exhibits a discontinuous jump at the transition from fully thermal volume-law on the thermal side, to pure area-law on the MBL side.Recent experimental advances in synthesizing isolated quantum many-body systems, such as cold-atoms [1][2][3][4], trapped ions [5,6], or impurity spins in solids [7,8], have raised fundamental questions about the nature of statistical mechanics. Even when decoupled from external sources of dissipation, large interacting quantum systems tend to act as their own heat-baths and reach thermal equilibrium. This behavior is formalized in the eigenstate thermalization hypothesis (ETH) [9,10]. Generic excited eigenstates of such thermal systems are highly entangled, with the entanglement of a subregion scaling as the volume of that region ("volume law"). This results in incoherent, classical dynamics at long times. In contrast, strong disorder can dramatically alter this picture by pinning excitations that would otherwise propagate heat and entanglement [11][12][13][14][15][16][17]. In such many-body localized (MBL) systems [18][19][20], generic eigenstates have properties akin to those of ground states. They exhibit short-range entanglement that scales like the perimeter of the subregion [17] ("area law"), and have quantum coherent dynamics up to arbitrarily long time scales [21][22][23][24][25][26][27], even at high energy densities [17,26,[28][29][30][31].A transition between MBL and thermal regimes requires a singular rearrangement of eigenstates from area-law to volume-law entanglement. This many-body (de)localization transition (MBLT) represents an entirely new class of critical phenomena, outside the conventional framework of equilibrium thermal or quantum phase transitions. Developing a systematic theory of this transition promises not only to expand our understanding of possible critical phenomena, but also to yield universal insights into the nature of the proximate MBL and thermal phases.The eigenstate entanglement entropy can be viewed as a non-equilibrium analog of the thermodynamic free energy for a conventional thermal phase transition, and plays a central role in our conceptual understanding of the MBL and ETH phases. Describing the entanglement across the MBLT requires addressing the challenging combination of disorder, interactio...

show abstract

Rare‐region effects and dynamics near the many‐body localization transition

Cited by 203 publications

References 119 publications

Transport in quasiperiodic interacting systems: From superdiffusion to subdiffusion

Transport in quasiperiodic interacting systems: From superdiffusion to subdiffusion

Many-body localization of bosons in optical lattices

Scaling Theory of Entanglement at the Many-Body Localization Transition

Contact Info

Product

Resources

About