Many-body localization in a quasiperiodic system

Iyer, Shankar; Oganesyan, Vadim; Refael, Gil; Huse, David A.

doi:10.1103/physrevb.87.134202

Cited by 421 publications

(404 citation statements)

References 59 publications

Supporting

Mentioning

389

Contrasting

Unclassified

Order By: Relevance

“…It will be interesting to see if this behavior is substantially different for models that are strongly nonintegrable at zero disorder. Another interesting followup on this work will be to look at models where the field is quasiperiodic [66,96] instead of random. Nonrandom quasiperiodic models should not have Griffiths rare regions so may remain diffusive throughout the thermal phase, or at least to much closer to the MBL phase transition.…”

Section: Numerical Evidencementioning

confidence: 99%

“…If the system has a putative many-body mobility edge separating MBL and thermal energy ranges, a state that is globally deep in the MBL energy range can have a local energy fluctuation that takes it to, or beyond, the energy density corresponding to the many-body mobility edge. Unlike rare regions of the disorder potential, rare regions of the state do not depend on the existence of quenched randomness, and could also apply to nonrandom quasiperiodic systems that show MBL [66].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

et al. 2017

Self Cite

View full text Add to dashboard Cite

The low-frequency response of systems near the many-body localization phase transition, on either side of the transition, is dominated by contributions from rare regions that are locally "in the other phase", i.e., rare localized regions in a system that is typically thermal, or rare thermal regions in a system that is typically localized. Rare localized regions affect the properties of the thermal phase, especially in one dimension, by acting as bottlenecks for transport and the growth of entanglement, whereas rare thermal regions in the localized phase act as local "baths" and dominate the low-frequency response of the MBL phase. We review recent progress in understanding these rare-region effects, and discuss some of the open questions associated with them: in particular, whether and in what circumstances a single rare thermal region can destabilize the many-body localized phase.

show abstract

Section: Numerical Evidencementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

et al. 2017

Self Cite

View full text Add to dashboard Cite

show abstract

“…where the ith component of m(t ) is the expectation value of σ z i at time t. This definition of the imbalance is the direct generalization of that typically used when the initial state is only taken to be one with a charge-density-wave ordering [64][65][66][67].…”

mentioning

confidence: 99%

“…This Hamiltonian exhibits a transition between a delocalized and a many-body localized state at a critical disorder strength that depends on the energy density of the state under consideration [60][61][62][63]. The dynamics of initial product states of spin polarization differs substantially between the two phases: While spins in the many-body localized phase retain a long-term correlation with their initial configuration, in the delocalized phase this correlation is lost over time as expected from an ergodic system [64][65][66][67]. In what follows we will be considering the dynamics of initial states that evolve in time under the Hamiltonian of Eq.…”

mentioning

confidence: 99%

Learning phase transitions from dynamics

2018

Self Cite

View full text Add to dashboard Cite

We propose the use of recurrent neural networks for classifying phases of matter based on the dynamics of experimentally accessible observables. We demonstrate this approach by training recurrent networks on the magnetization traces of two distinct models of one-dimensional disordered and interacting spin chains. The obtained phase diagram for a well-studied model of the many-body localization transition shows excellent agreement with previously known results obtained from time-independent entanglement spectra. For a periodically driven model featuring an inherently dynamical time-crystalline phase, the phase diagram that our network traces coincides with an order parameter for its expected phases.

show abstract

“…Implications of these results to experiments are discussed. PACS numbers: 73.20.Fz,03.65.Ud,71.10.Pm,73.21.Hb Many body localization (MBL) has drawn growing interest in recent years [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. The Anderson localization transition [21,22] is a zero-temperature quantum phase transition, which for the non-interacting case is manifested in the properties of the single-particle eigenstates and eigenvalues [23].…”

mentioning

confidence: 99%

Entanglement entropy of low-lying excitation in localized interacting system: Signature of Fock space delocalization

Berkovits

2014

Phys. Rev. B

View full text Add to dashboard Cite

The properties of the entanglement entropy (EE) of low-lying excitations in one-dimensional disordered interacting systems are studied. The ground state EE shows a clear signature of localization, while low-lying excitation shows a crossover from metallic behavior at short sample sizes to localized at longer length. The dependence of the crossover as function of interaction strength and sample length is studied using the density matrix renormalization group (DMRG). This behavior corresponds to the presence of the predicted many particle critical energy in the vicinity of the Fermi energy. Implications of these results to experiments are discussed. PACS numbers: 73.20.Fz,03.65.Ud,71.10.Pm,73.21.Hb Many body localization (MBL) has drawn growing interest in recent years [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. The Anderson localization transition [21,22] is a zero-temperature quantum phase transition, which for the non-interacting case is manifested in the properties of the single-particle eigenstates and eigenvalues [23]. For one and two dimensional systems all the single-particle state are localized for any amount of disorder, while for three dimensional systems at a given disorder there exists a critical energy (mobility edge) below which all states are localized. For a many-particle system, as long as no particleparticle interactions are present, the properties of a many-particle excited state are determined by the properties of the single-particle states. Thus, as long as all the particles occupy localized single-particle states the manyparticle states should exhibit localized behavior. For example, the entanglement entropy (EE) between any subregion A of the system and the rest of it should saturate (i.e., S A ∝ ξ d−1 , where d is the dimensionality of the system and ξ is the single-electron localization length). While if some of the extended single-particle states are occupied the usual volume law for the EE (S A ∝ L d A , where L A is the length of region A) is observed [17]. Physically, the difference between the localized and extended many-particle states is manifested in the dynamics of a particle tunneling into some particular region of the system, or a particle excited by a confined external perturbation in the region. In the localized phase it will remain there (i.e., will have a very long lifetime -sharp level), while in the extended case it will leave the region (short lifetime -broad level).What is the influence of particle-particle interaction on the above picture? A cursory consideration may lead to the conclusion that since particles now interact with each other, any localized excitation will eventually spread all over the system. Thus, the rest of the system acts as a thermal bath for any excited sub-system [24][25][26]. Surprisingly, Basko, Aleiner and Altshuler [2] have shown that if all the single-electron states are localized, an excitation will remain localized even in the presence of particleparticle interactions up to a critical temperature or excitatio...

show abstract

Many-body localization in a quasiperiodic system

Cited by 421 publications

References 59 publications

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

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

Learning phase transitions from dynamics

Entanglement entropy of low-lying excitation in localized interacting system: Signature of Fock space delocalization

Contact Info

Product

Resources

About