Ergodicity breaking in a model showing many-body localization

By Andrea De Luca, Antonello Scardicchio. 2012

230 citations recorded by the source corpus.

We study the breaking of ergodicity measured in terms of return probability in the evolution of a quantum state of a spin chain. In the non-ergodic phase a quantum state evolves in a much smaller fraction of the Hilbert space than would be allowed by the conservation of extensive observables. By the anomalous scaling of the participation ratios with system size we are led to consider the distribution of the wave function coefficients, a standard observable in modern studies of Anderson localization. We finally present a criterion for the identification of the ergodicity-breaking (many-body localization) transition based on these distributions which is quite robust and well suited for numerical investigations of a broad class of problems.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/8a3cf4a659b726abab5f476e10b1c120d6e73344

How researchers see this paper

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

In Artificial Intelligence

1. V. Ros
2. J. Imbrie
3. Maksym Serbyn
4. J. Moore
5. Antonello Scardicchio
6. Markus P. Müller

In Atomic and Molecular Physics, and Optics

1. J. Imbrie
2. V. Ros
3. Antonello Scardicchio
4. Maksym Serbyn
5. J. Moore
6. Markus P. Müller
7. D. Abanin
8. V. Khemani

Citations in the corpus

• Integrals of motion in the many-body localized phase (2014, background): “Since the seminal work by Basko, Aleiner and Altshuler [9, 4, 10], the paradigm of many-body localization has attracted a lot of interest, and the phenomenology of MBL phases and the localization transition have been explored, see for example [11, 12, 13, 14, 15, 16, 17]).”
• Spectral statistics across the many-body localization transition (2015, background): “[16, 17] report the onset of ergodicity breaking at the same location).”
• Criterion for Many-Body Localization-Delocalization Phase Transition (2015, unknown): “[21] A De Luca and A Scardicchio, Ergodicity breaking in a model showing many-body localization, Europhys.”
• Local integrals of motion in many‐body localized systems (2016, methodology): “Subsequently, a large body of numerical works has revealed the occurrence of localization in one dimensional systems of interacting fermions on a lattice and spin chains in random fields [11, 16, 33, 43, 62, 66, 71, 79, 80, 101, 106].”