FOR 5522 PhD School on Nonergodic Quantum Dynamics

Scaling theory of many-body ergodicity breaking

Not scheduled

2h

HS 2 (Max Born Hörsaal) (Faculty of Physics)

Poster Session

Description

Scaling theory of localization in noninteracting systems established validity of one-parameter scaling hypothesis in the entire range from the ergodic to localized states.
It is expected that in the presence of interactions, the many-body ergodicity breaking transition gives rise to the breakdown of the one-parameter scaling.
Here, we argue that the one-parameter scaling hypothesis may still represent the relevant theoretical framework even in many-body systems.
Based on the insights from the quantum sun model of the avalanche theory for many-body ergodicity breaking, we introduce a theoretical framework that interpolates between the one-parameter scaling at the critical point and a nontrivial scaling in the vicinity of the ergodic fixed point.
In the latter, the irrelevant corrections amount to substitute the linear dimension $L$ with $L-L_0$, in which $L_0$ is finite, and hence supporting the resilient one-parameter scaling at $L\gg L_0$.