Universality and quantum criticality in quasiperiodic spin chains.

Area of Science:

• Condensed Matter Physics
• Statistical Mechanics
• Quantum Systems

Background:

• Quasiperiodic systems exhibit aperiodic yet deterministic behavior, leading to critical phenomena distinct from clean or disordered systems.
• Previous understanding of quasiperiodic criticality was limited to specific discrete quasiperiodic sequences.
• Generic quasiperiodic modulations presented a challenge for theoretical analysis.

Purpose of the Study:

• To investigate the behavior of generic quasiperiodic modulations in spin chains.
• To develop a method for analyzing critical points in quasiperiodic systems beyond special cases.
• To apply the developed method to various quasiperiodic spin models and many-body localization transitions.

Main Methods:

• Application of a real-space renormalization-group transformation to quasiperiodic spin chains.
• Identification of fixed points for a functional renormalization group.
• Asymptotic analysis of critical points.

Main Results:

• Generic quasiperiodic modulations were shown to flow to discrete sequences under renormalization-group transformation.
• These discrete sequences act as fixed points for the functional renormalization group.
• An asymptotically exact treatment of critical points in quasiperiodic systems was enabled.

Conclusions:

• The study provides a powerful new framework for analyzing quasiperiodic criticality.
• This approach offers exact insights into the critical behavior of quasiperiodic spin chains.
• The findings have implications for understanding phenomena like many-body localization in quasiperiodic environments.