Efficient Computation of Cumulant Evolution and Full Counting Statistics: Application to Infinite Temperature Quantum...

Area of Science:

• Quantum mechanics
• Statistical physics
• Condensed matter theory

Background:

• High-temperature quantum systems present computational challenges.
• Efficiently calculating quantum generating functions is crucial for understanding system dynamics.
• Full counting statistics provide insights into particle or energy transport.

Purpose of the Study:

• To introduce an efficient numerical method for computing quantum generating functions.
• To enable high-accuracy estimation of cumulants and reconstruction of full counting statistics.
• To explore quantum dynamics in 1D systems at high temperatures.

Main Methods:

• Development of a novel numerical technique for quantum generating functions.
• Application to one-dimensional quantum systems at high temperatures.
• Utilizing quantum generating functions to derive cumulants and full counting statistics.

Main Results:

• High-accuracy estimates for cumulants were obtained.
• Full counting statistics were successfully reconstructed.
• The method was demonstrated on the spin S=1/2 anisotropic Heisenberg chain, reaching unprecedented timescales.
• Results challenge the Kardar-Parisi-Zhang universality conjecture for isotropic integrable quantum spin chains.

Conclusions:

• The proposed numerical method is efficient for computing quantum generating functions in 1D systems.
• The technique provides accurate insights into quantum dynamics and statistics.
• The findings suggest a re-evaluation of universality in certain quantum spin chain models.