Many-body localization in one dimension as a dynamical renormalization group fixed point

TL;DR

This paper develops a dynamical real space renormalization group method to analyze many-body localization in one-dimensional spin chains and fermionic systems, revealing universal entanglement growth and emergent conserved quantities.

Contribution

It introduces a novel RG approach to describe the time evolution of many-body localized states as a dynamical fixed point, providing analytic insights into entanglement and transport properties.

Findings

Universal logarithmic entanglement growth delayed by inverse interaction strength.

Particle number fluctuations grow as log(log(t)), indicating blocked transport.

Identification of an emergent generalized Gibbs ensemble at the fixed point.

Abstract

We formulate a dynamical real space renormalization group approach to describe the time evolution of a random spin-1/2 chain, or interacting fermions, initialized in a state with fixed particle positions. Within this approach we identify a many-body localized state of the chain as a dynamical infinite randomness fixed point. Near this fixed point our method becomes asymptotically exact, allowing analytic calculation of time dependent quantities. In particular we explain the striking universal features in the growth of the entanglement seen in recent numerical simulations: unbounded logarithmic growth delayed by a time inversely proportional to the interaction strength. The particle number fluctuations by contrast exhibit much slower growth as log(log(t)) indicating blocked particle transport. Lack of true thermalization in the long time limit is attributed to an infinite set of approximate integrals of motion revealed in the course of the RG flow, which become asymptotically exact conservation laws at the fixed point. Hence we identify the many-body localized state with an emergent generalized Gibbs ensemble.