Related Experiment Video
Updated: Nov 4, 2025

Fabrication and Characterization of Disordered Polymer Optical Fibers for Transverse Anderson Localization of Light
Published on: July 29, 2013
Numerical Evidence for Many-Body Localization in Two and Three Dimensions
Eli Chertkov1, Benjamin Villalonga1, Bryan K Clark1
1Institute for Condensed Matter Theory and IQUIST and Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA.
Many-body localization (MBL) and its associated conserved quantities, ℓ-bits, are explored in higher dimensions. A new algorithm confirms MBL in 2D and 3D systems, suggesting transitions in these models.
Area of Science:
- Quantum Physics
- Condensed Matter Physics
- Statistical Mechanics
Background:
- Many-body localization (MBL) describes systems where statistical mechanics breaks down due to disorder and interactions.
- The phenomenon is linked to quasilocal, binary conserved quantities known as ℓ-bits.
- The existence of MBL and ℓ-bits in dimensions greater than one remains an open question.
Purpose of the Study:
- To develop an algorithm for finding approximate binary ℓ-bits in arbitrary dimensions.
- To investigate the presence of MBL and ℓ-bits in higher-dimensional quantum systems.
Main Methods:
- An adaptive algorithm was developed to generate operator bases for representing ℓ-bits.
- The algorithm was applied to 1D, 2D, and 3D disordered Heisenberg models and a 2D disordered hard-core Bose-Hubbard model.
Main Results:
- High-quality ℓ-bits were found in all studied models at large disorder strengths.
- Rapid changes in ℓ-bit distributions indicated potential MBL transitions.
- Transitions in 1D and 2D models aligned with previous critical disorder strength estimates.
Conclusions:
- The study provides evidence for MBL phenomenology in 2D and 3D systems.
- The developed algorithm successfully probes MBL in higher dimensions and various geometries.
- This work opens avenues for studying MBL beyond one-dimensional systems.
More Related Videos
11:03An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
08:55Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses
Published on: June 7, 2018
Related Concept Videos
First Law: Particles in Two-dimensional Equilibrium
Newton's first law tells us about...
First Law: Particles in One-dimensional Equilibrium
Reduced Mass Coordinates: Isolated Two-body Problem
Atomic Nuclei: Nuclear Spin State Population Distribution
Three-Dimensional Analysis of Strain
The Pauli Exclusion Principle