Dynamical Criticality of Magnetization Transfer in Integrable Spin Chains

Area of Science:

• Condensed Matter Physics
• Statistical Mechanics
• Quantum Field Theory

Background:

• Integrable spin chains exhibit anomalous fluctuations, violating the central limit theorem.
• Understanding anomalous counting statistics is crucial for characterizing complex quantum systems.

Purpose of the Study:

• To investigate anomalous counting statistics in the Landau-Lifshitz field theory.
• To analyze two distinct anomalous regimes with a dynamical critical point.
• To determine the universality class of superdiffusive spin transport in integrable spin chains.

Main Methods:

• Optimized numerical simulations using integrable space-time discretization.
• Extraction of algebraic growth exponents for time-dependent cumulants.
• Analysis of magnetization transfer statistics in different regimes.

Main Results:

• Algebraic growth exponents of cumulants attain threshold values in anomalous regimes.
• Non-Gaussian statistics of magnetization transfer in the easy-axis regime converge to charged single-file systems.
• A weakly non-Gaussian distribution is observed at the isotropic point.

Conclusions:

• Superdiffusive spin transport in integrable spin chains does not fit known dynamical universality classes.
• The findings highlight the complexity of statistical properties in quantum systems.
• This work provides insights into anomalous transport phenomena in condensed matter systems.