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Climbing the exponential wall of the many-body localization problem

Research project selected under the 2021 call for proposals

Principal Investigator : Nicolas LAFLORENCIE

Involved Teams :

  • LPT / FFC

Type of project : Disruptive Project

Date (start/end) : 2021 – 2024

(a) Schematic picture of the decimation of strong random fields. At each step, the Hilbert space breaks up into 2 disconnected parts. (b) Full spectrum of a small chain of L = 8 sites at high disorder, calculated for a few decimation steps.

We propose a new method to theoretically address the many-body localization (MBL) problem for large system sizes. The main idea to beat the exponential complexity of this high-energy many-body problem is to couple the Strong Disorder Renormalization Group (SDRG) method with exact numerical techniques, thus allowing for a numerical treatment of much larger system sizes as compared to the state of the art. Two main targets will be pursued: MBL beyond one dimension, and a systematic exploration of MBL criticality.
Given the impressive theoretical and experimental activity of this field, the expected output is very exciting.