Extended slow dynamical regime close to the many-body localization transition

By D. J. Luitz, N. Laflorencie, Fabien Alet. 2015

241 citations recorded by the source corpus.

Many-body localization is characterized by a slow logarithmic growth of the entanglement entropy after a global quantum quench while the local memory of an initial density imbalance remains at infinite time. We investigate how much the proximity of a many-body localized phase can influence the dynamics in the delocalized ergodic regime where thermalization is expected. Using an exact Krylov space technique, the out-of-equilibrium dynamics of the random-field Heisenberg chain is studied up to L=28 sites, starting from an initially unentangled high-energy product state. Within most of the delocalized phase, we find a sub-ballistic entanglement growth $S(t)\propto t^{1/z}$ with a disorder-dependent exponent $z\ge1$, in contrast with the pure ballistic growth $z=1$ of clean systems. At the same time, anomalous relaxation is also observed for the spin imbalance $I(t) \propto t^{-\zeta}$ with a continuously varying disorder-dependent exponent $\zeta$, vanishing at the transition. This provides a clear experimental signature for detecting this non-conventional regime.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/3b84a50a5bb92688ee9afa5fc6c273862ba18a93

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

1. A. Nahum
2. J. Ruhman
3. S. Gopalakrishnan
4. S. Vijay
5. V. Khemani
6. V. Ros
7. Romain Vasseur
8. D. Huse

In Condensed Matter Physics

1. A. Nahum
2. J. Ruhman
3. S. Gopalakrishnan
4. Romain Vasseur
5. S. Vijay
6. Antonello Scardicchio
7. V. Ros
8. I. Bloch

In Statistical and Nonlinear Physics

1. J. Ruhman
2. A. Nahum
3. Romain Vasseur
4. Antonello Scardicchio
5. V. Ros
6. S. Vijay
7. I. Bloch
8. J. Moore

Citations in the corpus

• Probing Slow Relaxation and Many-Body Localization in Two-Dimensional Quasiperiodic Systems (2017, background): “This would require identifying the regime where critical scaling holds and to understand the role of rare-regions in quasi-periodic versus real-random systems in determining the critical properties [33, 42, 43].”
• Quantum Entanglement Growth Under Random Unitary Dynamics (2016, methodology): “[20] shows the height and width h(t) and w(t) for the two protocols (averaged over 380 realisations for the Phase evolution and 200 realisations for the Universal evolution, and over bonds x with 20 < x < 480).”
• Nonequilibrium quantum dynamics and transport: from integrability to many-body localization (2016, background): “or in the algebraic relaxation of (sum) of local observables [120, 128] such as the charge imbalance used in recent cold atom experiments [6] to characterize the MBL phase.”
• Many-body localization: An introduction and selected topics (2017, unknown): “Physically, this results in dephasing being present in MBL, while it is not there for Anderson insulators. this framework, the goal is in principle now simple: find a probe of dephasing.”
• Local integrals of motion in many‐body localized systems (2016, background): “1 As opposed to the linear growth in clean integrable or non-integrable systems [22, 60] and to the sub-ballistic growth in disordered, delocalized systems close to the MBL phase [67, 103].”