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One-Dimensional Quasiperiodic Mosaic Lattice with Exact Mobility Edges
Yucheng Wang1,2,3, Xu Xia4, Long Zhang2,3
1Shenzhen Institute for Quantum Science and Engineering, and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China.
Physical Review Letters
|November 20, 2020
Summary
Researchers discovered exactly solvable one-dimensional models with mobility edges (MEs) in energy spectra. This work provides exact analytical results for MEs and state localization in quasiperiodic systems, enabling experimental exploration.
Area of Science:
- Condensed matter physics
- Quantum mechanics
- Disordered systems
Background:
- Mobility edges (MEs) define the transition between extended and localized states, crucial for understanding localization phenomena.
- Exact analytical solutions for MEs in one-dimensional (1D) quasiperiodic systems are scarce, limiting precise theoretical understanding.
- Quasiperiodic potentials in 1D lattices are key to exploring complex electronic behaviors.
Purpose of the Study:
- To uncover and analyze a class of exactly solvable 1D models exhibiting mobility edges.
- To provide exact analytical results for mobility edges and the localization properties of all spectral states.
- To propose an experimentally feasible method for realizing these models.
Main Methods:
- Developing exactly solvable 1D models with quasiperiodic on-site potentials.
- Calculating Lyapunov exponents using Avila's global theory for analytical solutions.
- Numerically verifying results by computing the fractal dimension of states.
Main Results:
- Identification of a novel class of exactly solvable 1D quasiperiodic models with mobility edges.
- Exact analytical determination of mobility edges and localization/delocalization features for all energy states.
- Numerical confirmation of analytical findings through fractal dimension calculations.
Conclusions:
- The study presents a breakthrough in understanding localization physics through exactly solvable models.
- The findings offer precise analytical insights into mobility edges in 1D quasiperiodic systems.
- A feasible experimental scheme using optical Raman lattices is proposed for validating these theoretical predictions.
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