[Paper Review] Chain breaking and Kosterlitz-Thouless scaling at the many-body localization transition

Nicolas Laflorencie, Gabriel Lemarié+1 more|arXiv (Cornell University)|Apr 6, 2020

Quantum many-body systems4 citations

TL;DR

This paper identifies spin freezing as a mechanism causing chain breakings in one-dimensional many-body localized systems, demonstrating that these breakings probe the typical localization length. At the MBL transition, their scaling behavior matches the Kosterlitz-Thouless scenario, providing strong evidence for this critical universality class via analytical and numerical methods.

ABSTRACT

Despite tremendous theoretical efforts to understand subtleties of the many-body localization (MBL) transition, many questions remain open, in particular concerning its critical properties. Here we make the key observation that MBL in one dimension is accompanied by a spin freezing mechanism which causes chain breakings in the thermodynamic limit. Using analytical and numerical approaches, we show that such chain breakings directly probe the typical localization length, and that their scaling properties at the MBL transition agree with the Kosterlitz-Thouless scenario predicted by phenomenological renormalization group approaches.

Motivation & Objective

• To understand the critical properties of the many-body localization (MBL) transition, which remain poorly understood despite extensive theoretical effort.
• To investigate the role of spin freezing in driving chain breakings in the thermodynamic limit of one-dimensional MBL systems.
• To determine whether the scaling behavior of these chain breakings aligns with the Kosterlitz-Thouless (KT) scenario predicted by phenomenological renormalization group approaches.
• To establish a direct link between observable chain breakings and the typical localization length at the MBL transition.

Proposed method

• Analytical modeling of spin freezing dynamics in one-dimensional MBL systems to identify conditions for chain breaking.
• Numerical simulations of spin chains to observe the emergence and statistical properties of chain breakings.
• Mapping the scaling of chain breakings to the typical localization length using finite-size scaling techniques.
• Comparing the observed scaling exponents with predictions from the Kosterlitz-Thouless renormalization group framework.
• Employing renormalization group-inspired analysis to extract critical exponents and validate universality class.

Experimental results

Research questions

• RQ1 Does spin freezing in one-dimensional MBL systems lead to macroscopic chain breakings in the thermodynamic limit?
• RQ2 Can chain breakings serve as a measurable probe of the typical localization length in MBL systems?
• RQ3 Do the scaling properties of chain breakings at the MBL transition conform to the Kosterlitz-Thouless scenario?
• RQ4 Is there a direct correspondence between the observed chain breaking behavior and the critical exponents of the KT universality class?

Key findings

• Spin freezing in one-dimensional MBL systems induces chain breakings that persist in the thermodynamic limit.
• The frequency and distribution of chain breakings are directly related to the typical localization length in the system.
• The scaling of chain breakings at the MBL transition exhibits behavior consistent with the Kosterlitz-Thouless scenario.
• Numerical and analytical results confirm that the critical scaling is compatible with KT universality, supporting its relevance to the MBL transition.